nam a22 5a 4500 10.4171/004 DE-4084 2004-01-31 a fot 00| 0| cr nn mmmmamaa 040131e20040131gw fot 00| 0|eng d 9783037195048 10.4171/004 doi DE-4084 PBK bicssc PB bicssc 53C05 msc 53C07 msc 58J32 msc Wehrheim aut Uhlenbeck Compactness. EMS Press 2004 1 online resource (219 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 1 2523-5184 Restricted to subscribers. https://ems.press/books This book gives a detailed account of the analytic foundations of gauge theory - Uhlenbecks compactness theorems for general connections and for Yang-Mills connections. It intends to guide graduate students into the analysis of Yang-Mills theory as well as to serve as a reference for researchers in the field. The book is largely self-contained. It contains a number of appendices (e.g. on Sobolev spaces of maps between manifolds) and an introductory part covering the Lp\-regularity theory for the inhomogenous Neumann problem. The two main parts contain the full proofs of Uhlenbecks weak and strong compactness theorems on closed manifolds as well as their generalizations to manifolds with boundary and noncompact manifolds. These parts include a number of useful analytic tools such as general patching constructions and local slice theorems. Calculus & mathematical analysis bicssc Mathematics bicssc Connections (general theory) msc Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) msc Boundary value problems on manifolds msc https://ems.press/doi/10.4171/004 cover image https://content.ems.press/assets/public/images/books/cover-1.png nam a22 5a 4500 10.4171/063 DE-4084 2008-06-26 a fot 00| 0| cr nn mmmmamaa 080626e20080626gw fot 00| 0|eng d 9783037195635 10.4171/063 doi DE-4084 PBMP bicssc 53D40 msc 32Q65 msc 53D12 msc 16E45 msc Seidel aut Fukaya Categories and Picard-Lefschetz Theory. EMS Press 2008 1 online resource (334 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 8 2943-4971 Restricted to subscribers. https://ems.press/books The central objects in the book are Lagrangian submanifolds and their invariants, such as Floer homology and its multiplicative structures, which together constitute the Fukaya category. The relevant aspects of pseudo-holomorphic curve theory are covered in some detail, and there is also a self-contained account of the necessary homological algebra. Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations, and contains many previously unpublished results. The book will be of interest to graduate students and researchers in symplectic geometry and mirror symmetry. **** Winner 2010 AMS Veblen Prize in Geometry **** Differential & Riemannian geometry bicssc Symplectic aspects of Floer homology and cohomology msc Pseudoholomorphic curves msc Lagrangian submanifolds; Maslov index msc Differential graded algebras and applications (associative algebraic aspects) msc https://ems.press/doi/10.4171/063 cover image https://content.ems.press/assets/public/images/books/cover-2.jpg nam a22 5a 4500 10.4171/000 DE-4084 2003-12-15 a fot 00| 0| cr nn mmmmamaa 031215e20031215gw fot 00| 0|eng d 9783037195000 10.4171/000 doi DE-4084 PBT bicssc PBF bicssc 05-02 msc 60-02 msc 05A16 msc 60C05 msc Arratia aut Logarithmic Combinatorial Structures: A Probabilistic Approach. EMS Press 2003 1 online resource (374 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Monographs in Mathematics (emm) 1 2523-5206 Restricted to subscribers. https://ems.press/books The elements of many classical combinatorial structures can be naturally decomposed into components. Permutations can be decomposed into cycles, polynomials over a finite field into irreducible factors, mappings into connected components. In all of these examples, and in many more, there are strong similarities between the numbers of components of different sizes that are found in the decompositions of \`typical' elements of large size. For instance, the total number of components grows logarithmically with the size of the element, and the size of the largest component is an appreciable fraction of the whole. This book explains the similarities in asymptotic behaviour as the result of two basic properties shared by the structures: the conditioning relation and the logarithmic condition. The discussion is conducted in the language of probability, enabling the theory to be developed under rather general and explicit conditions; for the finer conclusions, Stein's method emerges as the key ingredient. The book is thus of particular interest to graduate students and researchers in both combinatorics and probability theory. Probability & statistics bicssc Algebra bicssc Research exposition (monographs, survey articles) pertaining to combinatorics msc Research exposition (monographs, survey articles) pertaining to probability theory msc Asymptotic enumeration msc Combinatorial probability msc Barbour aut Tavaré aut https://ems.press/doi/10.4171/000 cover image https://content.ems.press/assets/public/images/books/cover-18.png nam a22 5a 4500 10.4171/003 DE-4084 2004-05-31 a fot 00| 0| cr nn mmmmamaa 040531e20040531gw fot 00| 0|eng d 9783037195031 10.4171/003 doi DE-4084 PBKJ bicssc 37-XX msc 58-XX msc Pesin aut Lectures on partial hyperbolicity and stable ergodicity. EMS Press 2004 1 online resource (128 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 1 2943-4971 Restricted to subscribers. https://ems.press/books This book is an introduction to the modern theory of partial hyperbolicity with applications to stable ergodicity theory of smooth dynamical systems. It provides a systematic treatment of the theory and describes all the basic concepts and major results that have been obtained in the area since its creation around the early 1970s. It can be used as a textbook for a graduate student course and is also of interest to professional mathematicians working in the field of dynamical systems and their applications. Differential calculus & equations bicssc Dynamical systems and ergodic theory msc Global analysis, analysis on manifolds msc https://ems.press/doi/10.4171/003 cover image https://content.ems.press/assets/public/images/books/cover-5.png nam a22 5a 4500 10.4171/001 DE-4084 2004-02-15 a fot 00| 0| cr nn mmmmamaa 040215e20040215gw fot 00| 0|eng d 9783037195017 10.4171/001 doi DE-4084 PB bicssc 94-01 msc 12-01 msc Høholdt aut A Course In Error-Correcting Codes. EMS Press 2004 1 online resource (201 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 2943-4955 Restricted to subscribers. https://ems.press/books This book is written as a text for a course aimed at 3rd or 4th year students. Only some familiarity with elementary linear algebra and probability is directly assumed, but some maturity is required. The students may specialize in discrete mathematics, computer science, or communication engineering. The book is also a suitable introduction to coding theory for researchers from related fields or for professionals who want to supplement their theoretical basis. The book gives the coding basics for working on projects in any of the above areas, but material specific to one of these fields has not been included. The chapters cover the codes and decoding methods that are currently of most interest in research, development, and application. They give a relatively brief presentation of the essential results, emphasizing the interrelations between different methods and proofs of all important results. A sequence of problems at the end of each chapter serves to review the results and give the student an appreciation of the concepts. In addition, some problems and suggestions for projects indicate direction for further work. The presentation encourages the use of programming tools for studying codes, implementing decoding methods, and simulating performance. Specific examples of programming exercises are provided on the book's home page. *This book has appeared in a [second edition](https://doi.org/10.4171/179) in 2017.* Mathematics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory msc Justesen aut https://ems.press/doi/10.4171/001 cover image https://content.ems.press/assets/public/images/books/cover-238.blob nam a22 5a 4500 10.4171/002 DE-4084 2004-02-28 a fot 00| 0| cr nn mmmmamaa 040228e20040228gw fot 00| 0|eng d 9783037195024 10.4171/002 doi DE-4084 PBF bicssc 17-01 msc 17B10 msc 17B20 msc 22E46 msc Onishchik aut Lectures on Real Semisimple Lie Algebras and Their Representations. EMS Press 2004 1 online resource (95 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda ESI Lectures in Mathematics and Physics (esi) 1 2943-4939 Restricted to subscribers. https://ems.press/books In 1914, E. Cartan posed the problem to find all irreducible real linear Lie algebras. An updated exposition of his work was given by Iwahori (1959). This theory reduces the classification of irreducible real representations of a real Lie algebra to a description of the so-called self-conjugate irreducible complex representations of this algebra and to the calculation of an invariant of such a representation (with values +1 or -1) which is called the index. Moreover, these two problems were reduced to the case when the Lie algebra is simple and the highest weight of its irreducible complex representation is fundamental. A complete case-by-case classification for all simple real Lie algebras was given (without proof) in the tables of Tits (1967). But actually a general solution of these problems is contained in a paper of Karpelevich (1955) (written in Russian and not widely known), where inclusions between real forms induced by a complex representation were studied. We begin with a simplified (and somewhat extended and corrected) exposition of the main part of this paper and relate it to the theory of Cartan-Iwahori. We conclude with some tables, where an involution of the Dynkin diagram which allows us to find self-conjugate representations is described and explicit formulas for the index are given. In a short addendum, written by J. v. Silhan, this involution is interpreted in terms of the Satake diagram. The book is aimed at students in Lie groups, Lie algebras and their representations, as well as researchers in any field where these theories are used. The reader is supposed to know the classical theory of complex semisimple Lie algebras and their finite dimensional representation; the main facts are presented without proofs in Section 1. In the remaining sections the exposition is made with detailed proofs, including the correspondence between real forms and involutive automorphisms, the Cartan decompositions and the conjugacy of maximal compact subgroups of the automorphism group. Algebra bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to nonassociative rings and algebras msc Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) msc Simple, semisimple, reductive (super)algebras msc Semisimple Lie groups and their representations msc https://ems.press/doi/10.4171/002 cover image https://content.ems.press/assets/public/images/books/cover-8.png nam a22 5a 4500 10.4171/005 DE-4084 2008-02-05 a fot 00| 0| cr nn mmmmamaa 080205e20080205gw fot 00| 0|eng d 9783037195055 10.4171/005 doi DE-4084 PB bicssc 83C05 msc 35L70 msc 35Q75 msc 53C50 msc 58J45 msc 83C40 msc 83C45 msc Christodoulou aut Mathematical Problems of General Relativity I. EMS Press 2008 1 online resource (157 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 6 2943-4971 Restricted to subscribers. https://ems.press/books General Relativity is a theory proposed by Einstein in 1915 as a unified theory of space, time and gravitation. It is based on and extends Newtons theory of gravitation as well as Newtons equations of motion. It is thus fundamentally rooted in classical mechanics. The theory can be seen as a development of Riemannian geometry, itself an extension of Gauss intrinsic theory of curved surfaces in Euclidean space. The domain of application of the theory is astronomical systems. One of the mathematical methods analyzed and exploited in the present volume is an extension of Noethers fundamental principle connecting symmetries to conserved quantities. This is involved at a most elementary level in the very definition of the notion of hyperbolicity for an Euler-Lagrange system of partial differential equations. Another method is the study and systematic use of foliations by characteristic (null) hypersurfaces, and is in the spirit of the approach of Roger Penrose in his incompleteness theorem. The methods have applications beyond general relativity to problems in fluid mechanics and, more generally, to the mechanics and electrodynamics of continuous media. The book is intended for advanced students and researchers seeking an introduction into the methods and applications of general relativity. Mathematics bicssc Einstein's equations (general structure, canonical formalism, Cauchy problems) msc Second-order nonlinear hyperbolic equations msc PDEs in connection with relativity and gravitational theory msc Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics msc Hyperbolic equations on manifolds msc Gravitational energy and conservation laws; groups of motions msc Quantization of the gravitational field msc https://ems.press/doi/10.4171/005 cover image https://content.ems.press/assets/public/images/books/cover-13.jpg nam a22 5a 4500 10.4171/006 DE-4084 2004-10-25 a fot 00| 0| cr nn mmmmamaa 041025e20041025gw fot 00| 0|eng d 9783037195062 10.4171/006 doi DE-4084 PBMP bicssc PBKJ bicssc 53Axx msc 58Jxx msc Chang aut Non-linear Elliptic Equations in Conformal Geometry. EMS Press 2004 1 online resource (100 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 2 2943-4971 Restricted to subscribers. https://ems.press/books Non-linear elliptic partial differential equations are an important tool in the study of Riemannian metrics in differential geometry, in particular for problems concerning the conformal change of metrics in Riemannian geometry. In recent years the role played by the second order semi-linear elliptic equations in the study of Gaussian curvature and scalar curvature has been extended to a family of fully non-linear elliptic equations associated with other symmetric functions of the Ricci tensor. A case of particular interest is the second symmetric function of the Ricci tensor in dimension four closely related to the Pfaffian. In these lectures, starting from the background material, the author reviews the problem of prescribing Gaussian curvature on compact surfaces. She then develops the analytic tools (e.g. higher order conformal invariant operators, Sobolev inequalities, blow-up analysis) in order to solve a fully nonlinear equation in prescribing the Chern-Gauss-Bonnet integrand on compact manifolds of dimension four. Differential & Riemannian geometry bicssc Differential calculus & equations bicssc Classical differential geometry msc Partial differential equations on manifolds; differential operators msc https://ems.press/doi/10.4171/006 cover image https://content.ems.press/assets/public/images/books/cover-7.png nam a22 5a 4500 10.4171/132 DE-4084 2014-01-18 a fot 00| 0| cr nn mmmmamaa 140118e20140118gw fot 00| 0|eng d 9783037196328 10.4171/132 doi DE-4084 PBKD bicssc PBMP bicssc 26-01 msc 30F25 msc 30F45 msc 30F60 msc 32G15 msc 32Q45 msc 51-01 msc 51K05 msc 51K10 msc 51M09 msc 51M10 msc 51F99 msc 52-01 msc 52A07 msc 52A41 msc 53-01 msc 53C70 msc 54-01 msc 54E35 msc Papadopoulos aut Metric Spaces, Convexity and Nonpositive Curvature ; Second edition. EMS Press 2014 1 online resource (320 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 6 2523-5141 Restricted to subscribers. https://ems.press/books This book is about metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function satisfies a convexity condition. It also contains a systematic introduction to metric geometry, as well as a detailed presentation of some facets of convexity theory that are useful in the study of nonpositive curvature. The concepts and the techniques are illustrated by many examples, in particular from hyperbolic geometry, Hilbert geometry and Teichmüller theory. For the second edition, some corrections and a few additions have been made, and the bibliography has been updated. For the first edition of this book, please click [here](https://doi.org/10.4171/010). Complex analysis, complex variables bicssc Differential & Riemannian geometry bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions msc Ideal boundary theory for Riemann surfaces msc Conformal metrics (hyperbolic, Poincaré, distance functions) msc Teichmüller theory for Riemann surfaces msc Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) msc Hyperbolic and Kobayashi hyperbolic manifolds msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry msc General theory of distance geometry msc Synthetic differential geometry msc Elementary problems in hyperbolic and elliptic geometries msc Hyperbolic and elliptic geometries (general) and generalizations msc Metric geometry msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to convex and discrete geometry msc Convex sets in topological vector spaces (aspects of convex geometry) msc Convex functions and convex programs in convex geometry msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry msc Direct methods (\(G\)-spaces of Busemann, etc.) msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general topology msc Metric spaces, metrizability msc https://ems.press/doi/10.4171/132 cover image https://content.ems.press/assets/public/images/books/cover-16.jpg nam a22 5a 4500 10.4171/009 DE-4084 2005-06-30 a fot 10| 0| cr nn mmmmamaa 050630e20050630gw fot 10| 0|eng d 9783037195093 10.4171/009 doi DE-4084 PB bicssc Laptev edt European Congress of Mathematics ; Stockholm, June 27 - July 2, 2004. EMS Press 2005 1 online resource (897 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books The European Congress of Mathematics, held every four years, has established itself as a major international mathematical event. Following those in Paris, 1992, Budapest, 1996 and Barcelona, 2000, the Fourth European Congress of Mathematics took place in Stockholm, Sweden, June 27 to July 2, 2004 with 913 participants from 65 countries. Apart from seven plenary and thirty three invited lectures, there were six Science Lectures covering the most relevant aspects of mathematics in science and technology. Moreover, twelve projects of the EU Research Training Networks in Mathematics and Information Sciences, as well as Programmes from the European Science Foundation in Physical and Engineering Sciences were presented. Ten EMS Prizes were awarded to young European mathematicians who have made a particular contribution to the progress of mathematics. Five of the prize winners were independently chosen by the 4ECM Scientific Committee as plenary or invited speakers. The other five prize winners gave their lectures in parallel sessions. Most of these contributions are now collected in this volume, providing a permanent record of so much that is best in mathematics today. Plenary lectures * François Golse (Paris, France) * Francesco Guerra (Roma, Italy) * Johan Håstad (Stockholm, Sweden) * Andrei Okounkov (Princeton, USA) * Oded Schramm (Microsoft Research, USA) * Zoltán Szabó (Princeton, USA) * Claire Voisin (Paris, France) Invited Lectures * Giovanni Alberti (Pisa, Italy) * Denis Auroux (MIT, USA and Palaiseau, France)Stefano Bianchini (Rome, Italy) * François Bouchut (Paris, France) * Brian Bowditch (Southampton, UK) * Ehud Friedgut (Jerusalem, Israel) * Patrick Gérard (Orsay, France) * Alice Guionnet (Lyon, France) * Stefan Helmke (Kyoto, Japan) * Helge Holden (Trondheim, Norway) * Rupert Klein (Berlin, Germany) * Jan Krajícek (Prague, Czech Republic) * Daan Krammer (Warwick, UK) * Elon Lindenstrauss (Clay Mathematics Institute, USA) * Tomasz Luczak (Poznan, Poland) * Terry Lyons (Oxford, UK) * Pascal Massart (Orsay, France) * Preda Mihailescu (Paderborn, Germany) * Mircea Mustata (Clay Mathematics Institute, USA) * Kieran O'Grady (Roma , Italy) * Grigori Olshanski (Moscow, Russia) * Imre Ruzsa (Budapest, Hungary) * Yehuda Shalom (Tel-Aviv, Israel) * Maria Shcherbina (Kharkov, Ukraine) * Stanislav Smirnov (Stockholm, Sweden) * Mikhail Sodin (Tel-Aviv, Israel) * Xavier Tolsa (Barcelona, Spain) * Anna-Karin Tornberg (New York, USA and Stockholm, Sweden) * Vilmos Totik (Tampa, USA and Szeged, Hungary) * Michael Weiss (Aberdeen, UK) * Wendelin Werner (Orsay, France) * Umberto Zannier (Venice, Italy) Network lectures * Aline Bonami (Orléans, France) * Yann Brenier (Nice, France) * Jean Esterle (Bordeaux, France) * Bernard Helffer (Orsay, France) * Frank den Hollander (Eindhoven, Netherlands) * Jonathan Keating (Bristol, UK) * Christian Krattenthaler (Lyon, France) * Marina Monsurrò (Lausanne, Switzerland) * Jan Philip Solovej (Copenhagen, Denmark) * Miles Reid (Warwick, UK) * Jakob Stix (Bonn, Germany) Prize Lectures * Franck Barthe (Toulouse, France) * Paul Biran (Tel-Aviv, Israel) * Sylvia Serfaty (New York, USA) * Warwick Tucker (Uppsala, Sweden) * Otmar Venjakob (Heidelberg, Germany) Mathematics bicssc https://ems.press/doi/10.4171/009 cover image https://content.ems.press/assets/public/images/books/cover-3.png nam a22 5a 4500 10.4171/012 DE-4084 2005-05-31 a fot 00| 0| cr nn mmmmamaa 050531e20050531gw fot 00| 0|eng d 9783037195123 10.4171/012 doi DE-4084 PBKS bicssc PB bicssc 65Mxx msc 76-XX msc 82-XX msc Cordier edt Numerical Methods for Hyperbolic and Kinetic Problems. EMS Press 2005 1 online resource (367 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 7 2523-5141 Restricted to subscribers. https://ems.press/books Hyperbolic and kinetic equations arise in a large variety of industrial problems. For this reason, the CEMRACS summer research center held at CIRM in Luminy in 2003 was devoted to this topic. During a six-week period, junior and senior researchers worked full time on several projects proposed by industry and academia. Most of this work was completed later on, and the results are now reported in the present book. The articles address modelling issues as well as the development and comparisons of numerical methods in different situations. The applications include multi-phase flows, plasma physics, quantum particle dynamics, radiative transfer, sprays and aeroacoustics. The text is aimed at researchers and engineers interested in modelling and numerical simulation of hyperbolic and kinetic problems arising from applications. Numerical analysis bicssc Mathematics bicssc Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems msc Fluid mechanics msc Statistical mechanics, structure of matter msc Goudon edt Gutnic edt Sonnendrücker edt https://ems.press/doi/10.4171/012 cover image https://content.ems.press/assets/public/images/books/cover-4.png nam a22 5a 4500 10.4171/021 DE-4084 2006-04-30 a fot 00| 0| cr nn mmmmamaa 060430e20060430gw fot 00| 0|eng d 9783037195215 10.4171/021 doi DE-4084 PBKJ bicssc 35Q30 msc 76F05 msc Kuksin aut Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions. EMS Press 2006 1 online resource (102 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 3 2943-4971 Restricted to subscribers. https://ems.press/books The book gives an account of recent achievements in the mathematical theory of two-dimensional turbulence, described by the 2D Navier-Stokes equation, perturbed by a random force. The main results presented here were obtained during the last five to ten years and, up to now, have been available only in papers in the primary literature. Their summary and synthesis here, beginning with some preliminaries on partial differential equations and stochastics, make the book a self-contained account that will appeal to readers with a general background in analysis. After laying the groundwork, the author goes on to recent results on ergodicity of random dynamical systems, which the randomly forced Navier-Stokes equation defines in the function space of divergence-free vector fields, including a Central Limit Theorem. The physical meaning of these results is discussed as well as their relations with the theory of attractors. Next, the author studies the behaviour of solutions when the viscosity goes to zero. In the final section these dynamical methods are used to derive the so-called balance relations - the infinitely many algebraical relations satisfied by the solutions. Differential calculus & equations bicssc Navier-Stokes equations msc Isotropic turbulence; homogeneous turbulence msc https://ems.press/doi/10.4171/021 cover image https://content.ems.press/assets/public/images/books/cover-6.jpg nam a22 5a 4500 10.4171/013 DE-4084 2005-05-31 a fot 00| 0| cr nn mmmmamaa 050531e20050531gw fot 00| 0|eng d 9783037195130 10.4171/013 doi DE-4084 PBMP bicssc PBKJ bicssc 53Cxx msc 81Txx msc 58J60 msc 83D05 msc Biquard edt AdS/CFT Correspondence: Einstein Metrics and Their Conformal Boundaries. EMS Press 2005 1 online resource (259 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 8 2523-5141 Restricted to subscribers. https://ems.press/books Since its discovery in 1997 by Maldacena, AdS/CFT correspondence has become one of the prime subjects of interest in string theory, as well as one of the main meeting points between theoretical physics and mathematics. On the physical side it provides a duality between a theory of quantum gravity and a field theory. The mathematical counterpart is the relation between Einstein metrics and their conformal boundaries. The correspondence has been intensively studied, and a lot of progress emerged from the confrontation of viewpoints between mathematics and physics. Written by leading experts and directed at research mathematicians and theoretical physicists as well as graduate students, this volume gives an overview of this important area both in theoretical physics and in mathematics. It contains survey articles giving a broad overview of the subject and of the main questions, as well as more specialized articles providing new insight both on the Riemannian side and on the Lorentzian side of the theory. Differential & Riemannian geometry bicssc Differential calculus & equations bicssc Global differential geometry msc Quantum field theory; related classical field theories msc Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) msc Relativistic gravitational theories other than Einstein's, including asymmetric field theories msc https://ems.press/doi/10.4171/013 cover image https://content.ems.press/assets/public/images/books/cover-9.png nam a22 5a 4500 10.4171/011 DE-4084 2006-01-10 a fot 01| 0| cr nn mmmmamaa 060110e20060110gw fot 01| 0|eng d 9783037195116 10.4171/011 doi DE-4084 PBK bicssc PB bicssc Hjorth edt Dynamics on the Riemann Sphere ; A Bodil Branner Festschrift. EMS Press 2006 1 online resource (226 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books _Dynamics on the Riemann Sphere_ presents a collection of original research articles by leading experts in the area of holomorphic dynamics. These papers arose from the symposium _Dynamics in the Complex Plane_, held on the occasion of the 60th birthday of Bodil Branner. Topics covered range from Lattès maps to cubic polynomials over rational maps with Sierpinsky Carpets and Gaskets as Julia sets, as well as rational and entire transcendental maps with Herman rings. Contributors include Artur Avila (Paris VI, France), Arnault Chéritat (Toulouse, France), Robert L. Devaney (Boston, USA), Adrien Douady (Orsay, France), Nuria Fagella (Barcelona, Spain), Christian Henriksen (Lyngby, Denmark), Wolf Jung (Aachen, Germany), Tomoki Kawahira (Kyoto, Japan), Tan Lei (Cergy Pontoise, France), Mikhail Lyubich (Stony Brook, USA), Carsten Lunde Petersen (Roskilde, Denmark), John Milnor (Stony Brook, USA), Pascale Roesch (Lille, France). Calculus & mathematical analysis bicssc Mathematics bicssc Lunde Petersen edt https://ems.press/doi/10.4171/011 cover image https://content.ems.press/assets/public/images/books/cover-10.gif nam a22 5a 4500 10.4171/014 DE-4084 2005-08-30 a fot 00| 0| cr nn mmmmamaa 050830e20050830gw fot 00| 0|eng d 9783037195147 10.4171/014 doi DE-4084 PB bicssc Trzeciak aut Writing Mathematical Papers in English ; a practical guide. EMS Press 2005 1 online resource (51 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books This booklet is intended to provide practical help for authors of mathematical papers. It is written mainly for non-English speaking writers but should prove useful even to native speakers of English who are beginning their mathematical writing and may not yet have developed a command of the structure of mathematical discourse. The first part provides a collection of ready-made sentences and expressions occurring in mathematical papers. The examples are divided into sections according to their use (in introductions, definitions, theorems, proofs, comments, references to the literature, acknowledgements, editorial correspondence and referee's reports). Typical errors are also pointed out. The second part concerns selected problems of English grammar and usage, most often encountered by mathematical writers. Just as in the first part, an abundance of examples are presented, all of them taken from actual mathematical texts. The author has packed an awful lot in a few pages and has obviously been collecting his best (or worst) examples for a long time. Edwin F. Beschler About the author: Jerzy Trzeciak, formerly of Polish Scientific Publishers, is now the senior copy editor at the Institute of Mathematics, Polish Academy of Sciences. He is responsible for journals including Studia Mathematica, Fundamenta Mathematicae, Acta Arithmetica and others. He is also the author of Mathematical English Usage - a Dictionary, available at [IMPAN](https://drive.google.com/file/d/13OCm1qeegnua-7X6bslecQ0KPw5zQrka/view). Mathematics bicssc https://ems.press/doi/10.4171/014 cover image https://content.ems.press/assets/public/images/books/cover-11.png nam a22 5a 4500 10.4171/015 DE-4084 2006-02-14 a fot 00| 0| cr nn mmmmamaa 060214e20060214gw fot 00| 0|eng d 9783037195154 10.4171/015 doi DE-4084 PBMW bicssc 14H52 msc 14K25 msc Ekedahl aut One Semester of Elliptic Curves. EMS Press 2006 1 online resource (138 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 2 2523-5184 Restricted to subscribers. https://ems.press/books These lecture notes grew out of a one semester introductory course on elliptic curves given to an audience of computer science and mathematics students, and assume only minimal background knowledge. After having covered basic analytic and algebraic aspects, putting special emphasis on explaining the interplay between algebraic and analytic formulas, they go on to some more specialized topics. These include the j\-function from an algebraic and analytic perspective, a discussion of elliptic curves over finite fields, derivation of recursion formulas for the division polynomials, the algebraic structure of the torsion points of an elliptic curve, complex multiplication, and modular forms. In an effort to motivate basic problems the book starts very slowly, but considers some aspects such as modular forms of higher level which are not usually treated. It presents more than 100 exercises and a Mathematica notebook that treats a number of calculations involving elliptic curves. The book is aimed at students of mathematics with a general interest in elliptic curves but also at students of computer science interested in their cryptographic aspects. Algebraic geometry bicssc Elliptic curves msc Theta functions and abelian varieties msc https://ems.press/doi/10.4171/015 cover image https://content.ems.press/assets/public/images/books/cover-12.gif nam a22 5a 4500 10.4171/017 DE-4084 2006-02-28 a fot 00| 0| cr nn mmmmamaa 060228e20060228gw fot 00| 0|eng d 9783037195178 10.4171/017 doi DE-4084 PBKS bicssc PBKJ bicssc PBKJ bicssc 34A09 msc 65L80 msc Kunkel aut Differential-Algebraic Equations ; Analysis and Numerical Solution. EMS Press 2006 1 online resource (385 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 1 2943-4955 Restricted to subscribers. https://ems.press/books Differential-algebraic equations are a widely accepted tool for the modeling and simulation of constrained dynamical systems in numerous applications, such as mechanical multibody systems, electrical circuit simulation, chemical engineering, control theory, fluid dynamics and many others. This is the first comprehensive textbook that provides a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations. The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear systems. Further sections on control problems, generalized inverses of differential-algebraic operators, generalized solutions, and differential equations on manifolds complement the theoretical treatment of initial value problems. Two major classes of numerical methods for differential-algebraic equations (Runge--Kutta and BDF methods) are discussed and analyzed with respect to convergence and order. A chapter is devoted to index reduction methods that allow the numerical treatment of general differential-algebraic equations. The analysis and numerical solution of boundary value problems for differential-algebraic equations is presented, including multiple shooting and collocation methods. A survey of current software packages for differential-algebraic equations completes the text. The book is addressed to graduate students and researchers in mathematics, engineering and sciences, as well as practitioners in industry. A prerequisite is a standard course on the numerical solution of ordinary differential equations. Numerous examples and exercises make the book suitable as a course textbook or for self-study. This book has appeared in a [second edition](https://doi.org/10.4171/etb/28) in 2024. Numerical analysis bicssc Differential calculus & equations bicssc Differential calculus & equations bicssc Implicit ordinary differential equations, differential-algebraic equations msc Numerical methods for differential-algebraic equations msc Mehrmann aut https://ems.press/doi/10.4171/017 cover image https://content.ems.press/assets/public/images/books/cover-14.gif nam a22 5a 4500 10.4171/016 DE-4084 2006-02-28 a fot 00| 0| cr nn mmmmamaa 060228e20060228gw fot 00| 0|eng d 9783037195161 10.4171/016 doi DE-4084 PBPD bicssc PB bicssc 22D05 msc 22-01 msc 20E18 msc 22A25 msc 22B05 msc 22C05 msc 22D10 msc 22D45 msc 22F05 msc 12J10 msc 43A05 msc 54H15 msc 22A15 msc Stroppel aut Locally Compact Groups. EMS Press 2006 1 online resource (312 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 2 2943-4955 Restricted to subscribers. https://ems.press/books Locally compact groups play an important role in many areas of mathematics as well as in physics. The class of locally compact groups admits a strong structure theory, which allows to reduce many problems to groups constructed in various ways from the additive group of real numbers, the classical linear groups and from finite groups. The book gives a systematic and detailed introduction to the highlights of that theory. In the beginning, a review of fundamental tools from topology and the elementary theory of topological groups and transformation groups is presented. Completions, Haar integral, applications to linear representations culminating in the Peter-Weyl Theorem are treated. Pontryagin duality for locally compact Abelian groups forms a central topic of the book. Applications are given, including results about the structure of locally compact Abelian groups, and a structure theory for locally compact rings leading to the classification of locally compact fields. Topological semigroups are discussed in a separate chapter, with special attention to their relations to groups. The last chapter reviews results related to Hilbert's Fifth Problem, with the focus on structural results for non-Abelian connected locally compact groups that can be derived using approximation by Lie groups. The book is self-contained and is addressed to advanced undergraduate or graduate students in mathematics or physics. It can be used for one-semester courses on topological groups, on locally compact Abelian groups, or on topological algebra. Suggestions on course design are given in the preface. Each chapter is accompanied by a set of exercises that have been tested in classes. Algebraic topology bicssc Mathematics bicssc General properties and structure of locally compact groups msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to topological groups msc Limits, profinite groups msc Representations of general topological groups and semigroups msc General properties and structure of LCA groups msc Compact groups msc Unitary representations of locally compact groups msc Automorphism groups of locally compact groups msc General theory of group and pseudogroup actions msc Valued fields msc Measures on groups and semigroups, etc. msc Transformation groups and semigroups (topological aspects) msc Structure of topological semigroups msc https://ems.press/doi/10.4171/016 cover image https://content.ems.press/assets/public/images/books/cover-15.jpg nam a22 5a 4500 10.4171/022 DE-4084 2007-05-15 a fot 10| 0| cr nn mmmmamaa 070515e20070515gw fot 10| 0|eng d 9783037195222 10.4171/022 doi DE-4084 PB bicssc 00Bxx msc Sanz-Solé edt Proceedings of the International Congress of Mathematicians Madrid, August 22-30, 2006. EMS Press 2007 1 online resource (4392 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books **Note: The ICM2006 Proceedings are available only as a set, individual volumes cannot be ordered.** The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world, and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress. The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject. Mathematics bicssc Conference proceedings and collections of articles msc Soria edt Varona edt Verdera edt https://ems.press/doi/10.4171/022 cover image https://content.ems.press/assets/public/images/books/cover-17.png nam a22 5a 4500 10.4171/022-1 DE-4084 2007-05-15 a fot 10| 0| cr nn mmmmamaa 070515e20070515gw fot 10| 0|eng d 9783985475360 10.4171/022-1 doi DE-4084 PB bicssc 00Bxx msc Sanz-Solé edt Proceedings of the International Congress of Mathematicians Madrid, August 22-30, 2006. Volume I. Plenary Lectures and Ceremonies EMS Press 2007 1 online resource (4392 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books **Note: The ICM2006 Proceedings are available only as a set, individual volumes cannot be ordered.** The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world, and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress. The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject. Mathematics bicssc Conference proceedings and collections of articles msc Soria edt Varona edt Verdera edt https://ems.press/doi/10.4171/022-1 cover image https://content.ems.press/assets/public/images/books/cover-20.png nam a22 5a 4500 10.4171/022-2 DE-4084 2007-05-15 a fot 10| 0| cr nn mmmmamaa 070515e20070515gw fot 10| 0|eng d 9783985475377 10.4171/022-2 doi DE-4084 PB bicssc 00Bxx msc Sanz-Solé edt Proceedings of the International Congress of Mathematicians Madrid, August 22-30, 2006. Volume II. Invited Lectures EMS Press 2007 1 online resource (4392 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books **Note: The ICM2006 Proceedings are available only as a set, individual volumes cannot be ordered.** The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world, and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress. The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject. Mathematics bicssc Conference proceedings and collections of articles msc Soria edt Varona edt Verdera edt https://ems.press/doi/10.4171/022-2 cover image https://content.ems.press/assets/public/images/books/cover-21.png nam a22 5a 4500 10.4171/022-3 DE-4084 2007-05-15 a fot 10| 0| cr nn mmmmamaa 070515e20070515gw fot 10| 0|eng d 9783985475384 10.4171/022-3 doi DE-4084 PB bicssc 00Bxx msc Sanz-Solé edt Proceedings of the International Congress of Mathematicians Madrid, August 22-30, 2006. Volume III. Invited Lectures EMS Press 2007 1 online resource (4392 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books **Note: The ICM2006 Proceedings are available only as a set, individual volumes cannot be ordered.** The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world, and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress. The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject. Mathematics bicssc Conference proceedings and collections of articles msc Soria edt Varona edt Verdera edt https://ems.press/doi/10.4171/022-3 cover image https://content.ems.press/assets/public/images/books/cover-24.png nam a22 5a 4500 10.4171/023 DE-4084 2006-05-10 a fot 00| 0| cr nn mmmmamaa 060510e20060510gw fot 00| 0|eng d 9783037195239 10.4171/023 doi DE-4084 PBPD bicssc 55-01 msc Matveev aut Lectures on Algebraic Topology. EMS Press 2006 1 online resource (106 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 3 2523-5184 Restricted to subscribers. https://ems.press/books Algebraic topology is the study of the global properties of spaces by means of algebra. It is an important branch of modern mathematics with a wide degree of applicability to other fields, including geometric topology, differential geometry, functional analysis, differential equations, algebraic geometry, number theory, and theoretical physics. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding. The numerous illustrations in the text also serve this purpose. Two features make the text different from the standard literature: first, special attention is given to providing explicit algorithms for calculating the homology groups and for manipulating the fundamental groups. Second, the book contains many exercises, all of which are supplied with hints or solutions. This makes the book suitable for both classroom use and for independent study. Algebraic topology bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology msc https://ems.press/doi/10.4171/023 cover image https://content.ems.press/assets/public/images/books/cover-23.png nam a22 5a 4500 10.4171/024 DE-4084 2006-06-30 a fot 00| 0| cr nn mmmmamaa 060630e20060630gw fot 00| 0|eng d 9783037195246 10.4171/024 doi DE-4084 PBMP bicssc 58B34 msc 46L87 msc 81T75 msc Várilly aut An Introduction to Noncommutative Geometry. EMS Press 2006 1 online resource (121 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 4 2523-5184 Restricted to subscribers. https://ems.press/books Noncommutative geometry, inspired by quantum physics, describes singular spaces by their noncommutative coordinate algebras, and metric structures by Dirac-like operators. Such metric geometries are described mathematically by Connes' theory of spectral triples. These lectures, delivered at an EMS Summer School on noncommutative geometry and its applications, provide an overview of spectral triples based on examples. This introduction is aimed at graduate students of both mathematics and theoretical physics. It deals with Dirac operators on spin manifolds, noncommutative tori, Moyal quantization and tangent groupoids, action functionals, and isospectral deformations. The structural framework is the concept of a noncommutative spin geometry; the condiditons on spectral triples which determine this concept are developed in detail. The emphasis throughout is on gaining understanding by computing the details of specific examples. The book provides a middle ground between a comprehensive text and a narrowly focused research monograph. It is intended for self-study, enabling the reader to gain access to the essentials of noncommutative geometry. New features since the original course are an expanded bibliography and a survey of more recent examples and applications of spectral triples. Differential & Riemannian geometry bicssc Noncommutative geometry (à la Connes) msc Noncommutative differential geometry msc Noncommutative geometry methods in quantum field theory msc https://ems.press/doi/10.4171/024 cover image https://content.ems.press/assets/public/images/books/cover-22.png nam a22 5a 4500 10.4171/025 DE-4084 2006-07-10 a fot 00| 0| cr nn mmmmamaa 060710e20060710gw fot 00| 0|eng d 9783037195253 10.4171/025 doi DE-4084 PBMP bicssc 53C55 msc 32Q15 msc 32Qxx msc 58Jxx msc 53C35 msc Ballmann aut Lectures on Kähler Manifolds. EMS Press 2006 1 online resource (182 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda ESI Lectures in Mathematics and Physics (esi) 2 2943-4939 Restricted to subscribers. https://ems.press/books These notes are based on lectures the author held at the University of Bonn and the Erwin-Schrödinger-Institute in Vienna. The aim is to give a thorough introduction to the theory of Kähler manifolds with special emphasis on the differential geometric side of Kähler geometry. The exposition starts with a short discussion of complex manifolds and holomorphic vector bundles and a detailed account of the basic differential geometric properties of Kähler manifolds. The more advanced topics are the cohomology of Kähler manifolds, Calabi conjecture, Gromov's Kähler hyperbolic spaces, and the Kodaira embedding theorem. Some familiarity with global analysis and partial differential equations is assumed, in particular in the part on the Calabi conjecture. There are appendices on Chern-Weil theory, symmetric spaces, and _L2_\-cohomology. Differential & Riemannian geometry bicssc Global differential geometry of Hermitian and Kählerian manifolds msc Kähler manifolds msc Complex manifolds msc Partial differential equations on manifolds; differential operators msc Differential geometry of symmetric spaces msc https://ems.press/doi/10.4171/025 cover image https://content.ems.press/assets/public/images/books/cover-19.png nam a22 5a 4500 10.4171/027 DE-4084 2007-01-10 a fot 00| 0| cr nn mmmmamaa 070110e20070110gw fot 00| 0|eng d 9783037195277 10.4171/027 doi DE-4084 PBT bicssc PBWL bicssc 60F05 msc 60K35 msc 62C12 msc 62F05 msc 62F12 msc 62G30 msc 62Jxx msc Deheuvels aut Lectures on Empirical Processes ; Theory and Statistical Applications. EMS Press 2007 1 online resource (263 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 6 2523-5184 Restricted to subscribers. https://ems.press/books The theory of empirical processes constitutes the mathematical toolbox of asymptotic statistics. Its growth was accelerated by the 1950s work on the Functional Central Limit Theorem and the Invariance Principle. The theory has developed in parallel with statistical methodologies, and has been successfully applied to a large diversity of problems related to the asymptotic behaviour of statistical procedures. The three sets of lecture notes in the book offer a wide panorama of contemporary empirical processes theory. Techniques are developed in the framework of probability in Banach spaces, Hungarian-style strong approximations, using tools from general stochastic process theory. Other tools appear in this text in connection with historical as well as modern applications, such as goodness-of-fit tests, density estimation or general M-estimators. This book gives an excellent overview of the broad scope of the theory of empirical processes. It will be an invaluable aid for students and researchers interested in an advanced and well-documented approach to the selected topics. Probability & statistics bicssc Stochastics bicssc Central limit and other weak theorems msc Interacting random processes; statistical mechanics type models; percolation theory msc Empirical decision procedures; empirical Bayes procedures msc Asymptotic properties of parametric tests msc Asymptotic properties of parametric estimators msc Order statistics; empirical distribution functions msc Linear inference, regression msc del Barrio aut van de Geer aut https://ems.press/doi/10.4171/027 cover image https://content.ems.press/assets/public/images/books/cover-223.png nam a22 5a 4500 10.4171/030 DE-4084 2006-08-30 a fot 00| 0| cr nn mmmmamaa 060830e20060830gw fot 00| 0|eng d 9783037195307 10.4171/030 doi DE-4084 PBMP bicssc PBKJ bicssc 58J35 msc 53C21 msc 35K55 msc 58E11 msc 58E10 msc Müller aut Differential Harnack Inequalities and the Ricci Flow. EMS Press 2006 1 online resource (99 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 5 2523-5184 Restricted to subscribers. https://ems.press/books The classical Harnack inequalities play an important role in the study of parabolic partial differential equations. The idea of finding a differential version of such a classical Harnack inequality goes back to Peter Li and Shing Tung Yau, who introduced a pointwise gradient estimate for a solution of the linear heat equation on a manifold which leads to a classical Harnack type inequality if being integrated along a path. Their idea has been successfully adopted and generalized to (nonlinear) geometric heat flows such as mean curvature flow or Ricci flow; most of this work was done by Richard Hamilton. In 2002, Grisha Perelman presented a new kind of differential Harnack inequality which involves both the (adjoint) linear heat equation and the Ricci flow. This led to a completely new approach to the Ricci flow that allowed interpretation as a gradient flow which maximizes different entropy functionals. This approach forms the main analytic core of Perelmans attempt to prove the Poincaré conjecture. It is, however, of completely independent interest and may as well prove useful in various other areas, such as, for instance, the theory of Kähler manifolds. The goal of this book is to explain this analytic tool in full detail for the two examples of the linear heat equation and the Ricci flow. It begins with the original Li-Yau result, presents Hamilton's Harnack inequalities for the Ricci flow, and ends with Perelman's entropy formulas and space-time geodesics. The text is a self-contained, modern introduction to the Ricci flow and the analytic methods to study it. It is primarily addressed to students who have a basic introductory knowledge of analysis and of Riemannian geometry and who are attracted to further study in geometric analysis. No previous knowledge of differential Harnack inequalities or the Ricci flow is required. Differential & Riemannian geometry bicssc Differential calculus & equations bicssc Heat and other parabolic equation methods for PDEs on manifolds msc Methods of global Riemannian geometry, including PDE methods; curvature restrictions msc Nonlinear parabolic equations msc Critical metrics msc Variational problems in applications to the theory of geodesics (problems in one independent variable) msc https://ems.press/doi/10.4171/030 cover image https://content.ems.press/assets/public/images/books/cover-26.png nam a22 5a 4500 10.4171/028 DE-4084 2006-10-12 a fot 00| 0| cr nn mmmmamaa 061012e20061012gw fot 00| 0|eng d 9783037195284 10.4171/028 doi DE-4084 PH bicssc PB bicssc PBH bicssc 11Fxx msc 11Lxx msc 11Mxx msc 81Txx msc 52Cxx msc 68R15 msc Nyssen edt Physics and Number Theory. EMS Press 2006 1 online resource (274 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 10 2523-5141 Restricted to subscribers. https://ems.press/books There is a rich and historical relationship between theoretical physics and number theory. This volume presents a selection of problems which are currently in full development and inspire a lot of research going on. Each of the seven contributions starts with an introductory survey which makes it possible even for non-specialists to understand the results and to gain an idea of the great variety of subjects and techniques used. Topics covered are: phase locking in oscillating systems, crystallography, Hopf algebras and renormalisation theory, Zeta-function and random matrices, Kloosterman sums and the local Langlands correspondence. Intended for research mathematicians and theoretical physicists as well as graduate students, this volume gives an overview of recent developments in an exciting subject crossing several disciplines. Physics bicssc Mathematics bicssc Number theory bicssc Discontinuous groups and automorphic forms msc Exponential sums and character sums msc Zeta and \(L\)-functions: analytic theory msc Quantum field theory; related classical field theories msc Discrete geometry msc Combinatorics on words msc https://ems.press/doi/10.4171/028 cover image https://content.ems.press/assets/public/images/books/cover-27.png nam a22 5a 4500 10.4171/020 DE-4084 2006-12-01 a fot 00| 0| cr nn mmmmamaa 061201e20061201gw fot 00| 0|eng d 9783037195208 10.4171/020 doi DE-4084 PBKJ bicssc 14N15 msc 20F55 msc 32G34 msc 32S22 msc 33E17 msc 34Mxx msc 35C10 msc 35Q15 msc 70H05 msc 12Hxx msc 14H10 msc 14Pxx msc 17B37 msc 17B40 msc 17B67 msc 32S40 msc 35C20 msc 53C15 msc 53D30 msc 70G65 msc 82B23 msc Bertrand edt Differential Equations and Quantum Groups ; Andrey A. Bolibrukh Memorial Volume. EMS Press 2006 1 online resource (302 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 9 2523-5141 Restricted to subscribers. https://ems.press/books This special volume is dedicated to the memory of Andrey A. Bolibrukh. It contains two expository articles devoted to some aspects of Bolibrukh's work, followed by ten refereed research articles. Topics cover complex linear and nonlinear differential equations as well as quantum groups: monodromy, Fuchsian linear systems, Riemann-Hilbert problem, differential Galois theory, differential algebraic groups, multisummability, isomonodromy, Painlevé equations, Schlesinger equations, integrable systems, KZ equations, complex reflection groups, root systems. Differential calculus & equations bicssc Classical problems, Schubert calculus msc Reflection and Coxeter groups (group-theoretic aspects) msc Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) msc Relations with arrangements of hyperplanes msc Painlevé-type functions msc Ordinary differential equations in the complex domain msc Series solutions to PDEs msc Riemann-Hilbert problems in context of PDEs msc Hamilton's equations msc Differential and difference algebra msc Families, moduli of curves (algebraic) msc Real algebraic and real-analytic geometry msc Quantum groups (quantized enveloping algebras) and related deformations msc Automorphisms, derivations, other operators for Lie algebras and super algebras msc Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras msc Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects) msc Asymptotic expansions of solutions to PDEs msc General geometric structures on manifolds (almost complex, almost product structures, etc.) msc Symplectic structures of moduli spaces msc Symmetries, Lie group and Lie algebra methods for problems in mechanics msc Exactly solvable models; Bethe ansatz msc Enriquez edt Mitschi edt Sabbah edt Schäfke edt https://ems.press/doi/10.4171/020 cover image https://content.ems.press/assets/public/images/books/cover-28.png nam a22 5a 4500 10.4171/031 DE-4084 2007-01-10 a fot 00| 0| cr nn mmmmamaa 070110e20070110gw fot 00| 0|eng d 9783037195314 10.4171/031 doi DE-4084 PBKJ bicssc PHDF bicssc PB bicssc 35L67 msc 35L65 msc 35L70 msc 58J45 msc 76L05 msc 76N15 msc 76Y05 msc Christodoulou aut The Formation of Shocks in 3-Dimensional Fluids. EMS Press 2007 1 online resource (1000 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Monographs in Mathematics (emm) 2 2523-5206 Restricted to subscribers. https://ems.press/books The equations describing the motion of a perfect fluid were first formulated by Euler in 1752. These equations were among the first partial differential equations to be written down, but, after a lapse of two and a half centuries, we are still far from adequately understanding the observed phenomena which are supposed to lie within their domain of validity. These phenomena include the formation and evolution of shocks in compressible fluids, the subject of the present monograph. The first work on shock formation was done by Riemann in 1858. However, his analysis was limited to the simplified case of one space dimension. Since then, several deep physical insights have been attained and new methods of mathematical analysis invented. Nevertheless, the theory of the formation and evolution of shocks in real three-dimensional fluids has remained up to this day fundamentally incomplete. This monograph considers the relativistic Euler equations in three space dimensions for a perfect fluid with an arbitrary equation of state. We consider initial data for these equations which outside a sphere coincide with the data corresponding to a constant state. Under suitable restriction on the size of the initial departure from the constant state, we establish theorems that give a complete description of the maximal classical development. In particular, it is shown that the boundary of the domain of the maximal classical development has a singular part where the inverse density of the wave fronts vanishes, signalling shock formation. The theorems give a detailed description of the geometry of this singular boundary and a detailed analysis of the behavior of the solution there. A complete picture of shock formation in three-dimensional fluids is thereby obtained. The approach is geometric, the central concept being that of the acoustical spacetime manifold. The monograph will be of interest to people working in partial differential equations in general and in fluid mechanics in particular. Differential calculus & equations bicssc Fluid mechanics bicssc Mathematics bicssc Shocks and singularities for hyperbolic equations msc Hyperbolic conservation laws msc Second-order nonlinear hyperbolic equations msc Hyperbolic equations on manifolds msc Shock waves and blast waves in fluid mechanics msc Gas dynamics (general theory) msc Quantum hydrodynamics and relativistic hydrodynamics msc https://ems.press/doi/10.4171/031 cover image https://content.ems.press/assets/public/images/books/cover-29.jpg nam a22 5a 4500 10.4171/034 DE-4084 2007-03-03 a fot 00| 0| cr nn mmmmamaa 070303e20070303gw fot 00| 0|eng d 9783037195345 10.4171/034 doi DE-4084 PBMS bicssc 16G30 msc 70H06 msc 16S80 msc 14A22 msc Etingof aut Calogero-Moser systems and representation theory. EMS Press 2007 1 online resource (101 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 4 2943-4971 Restricted to subscribers. https://ems.press/books Calogero-Moser systems, which were originally discovered by specialists in integrable systems are currently at the crossroads of many areas of mathematics and within the scope of interests of many mathematicians. More specifically, these systems and their generalizations turned out to have intrinsic connections with such fields as algebraic geometry (Hilbert schemes of surfaces), representation theory (double affine Hecke algebras, Lie groups, quantum groups), deformation theory (symplectic reflection algebras), homological algebra (Koszul algebras), Poisson geometry, etc. The goal of the present lecture notes is to give an introduction to the theory of Calogero-Moser systems, highlighting their interplay with these fields. Since these lectures are designed for non-experts, we give short introductions to each of the subjects involved, and provide a number of exercises. The book will be suitable for mathematics graduate students and researchers in the areas of representation theory, noncommutative algebra, algebraic geometry, and related areas. Analytic geometry bicssc Representations of orders, lattices, algebras over commutative rings msc Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics msc Deformations of associative rings msc Noncommutative algebraic geometry msc https://ems.press/doi/10.4171/034 cover image https://content.ems.press/assets/public/images/books/cover-30.jpg nam a22 5a 4500 10.4171/038 DE-4084 2007-04-04 a fot 00| 0| cr nn mmmmamaa 070404e20070404gw fot 00| 0|eng d 9783037195383 10.4171/038 doi DE-4084 PB bicssc PBX bicssc 11-XX msc 12-XX msc Iwaniec edt Andrzej Schinzel, Selecta. EMS Press 2007 1 online resource (1417 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 1 2523-5222 Restricted to subscribers. https://ems.press/books Andrzej Schinzel, born in 1937, is a leading number theorist whose work has a lasting impact on modern mathematics. He is the author of over 200 research articles in various branches of arithmetics, including elementary, analytic and algebraic number theory. He has also been, for nearly 40 years, the editor of Acta Arithmetica, the first international journal devoted exclusively to number theory. These Selecta contain Schinzel's most important articles published between 1955 and 2006. The arrangement is by topic, with each major category introduced by an expert's comment. Many of the hundred selected papers deal with arithmetical and algebraic properties of polynomials in one or several variables, but there are also articles on Euler's totient function, the favorite subject of Schinzel's early research, on prime numbers (including the famous paper with Sierpiński on the Hypothesis H), algebraic number theory, diophantine equations, analytical number theory and geometry of numbers. Volume II concludes with some papers from outside number theory, as well as a list of unsolved problems and unproved conjectures, taken from the work of Schinzel. Mathematics bicssc History of mathematics bicssc Number theory msc Field theory and polynomials msc Narkiewicz edt Urbanowicz edt https://ems.press/doi/10.4171/038 cover image https://content.ems.press/assets/public/images/books/cover-31.jpg nam a22 5a 4500 10.4171/038-1 DE-4084 2007-04-04 a fot 00| 0| cr nn mmmmamaa 070404e20070404gw fot 00| 0|eng d 9783985475346 10.4171/038-1 doi DE-4084 PB bicssc 11-XX msc 12-XX msc Iwaniec edt Andrzej Schinzel, Selecta. Volume I. Diophantine Problems and Polynomials EMS Press 2007 1 online resource (1417 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 1 2523-5222 Restricted to subscribers. https://ems.press/books Andrzej Schinzel, born in 1937, is a leading number theorist whose work has a lasting impact on modern mathematics. He is the author of over 200 research articles in various branches of arithmetics, including elementary, analytic and algebraic number theory. He has also been, for nearly 40 years, the editor of Acta Arithmetica, the first international journal devoted exclusively to number theory. These Selecta contain Schinzel's most important articles published between 1955 and 2006. The arrangement is by topic, with each major category introduced by an expert's comment. Many of the hundred selected papers deal with arithmetical and algebraic properties of polynomials in one or several variables, but there are also articles on Euler's totient function, the favorite subject of Schinzel's early research, on prime numbers (including the famous paper with Sierpiński on the Hypothesis H), algebraic number theory, diophantine equations, analytical number theory and geometry of numbers. Volume II concludes with some papers from outside number theory, as well as a list of unsolved problems and unproved conjectures, taken from the work of Schinzel. Mathematics bicssc Number theory msc Field theory and polynomials msc Narkiewicz edt Urbanowicz edt https://ems.press/doi/10.4171/038-1 cover image https://content.ems.press/assets/public/images/books/cover-32.jpg nam a22 5a 4500 10.4171/038-2 DE-4084 2007-04-04 a fot 00| 0| cr nn mmmmamaa 070404e20070404gw fot 00| 0|eng d 9783985475353 10.4171/038-2 doi DE-4084 PB bicssc 11-XX msc 12-XX msc Iwaniec edt Andrzej Schinzel, Selecta. Volume II. Elementary, Analytic and Geometric Number Theory EMS Press 2007 1 online resource (1417 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 1 2523-5222 Restricted to subscribers. https://ems.press/books Andrzej Schinzel, born in 1937, is a leading number theorist whose work has a lasting impact on modern mathematics. He is the author of over 200 research articles in various branches of arithmetics, including elementary, analytic and algebraic number theory. He has also been, for nearly 40 years, the editor of Acta Arithmetica, the first international journal devoted exclusively to number theory. These Selecta contain Schinzel's most important articles published between 1955 and 2006. The arrangement is by topic, with each major category introduced by an expert's comment. Many of the hundred selected papers deal with arithmetical and algebraic properties of polynomials in one or several variables, but there are also articles on Euler's totient function, the favorite subject of Schinzel's early research, on prime numbers (including the famous paper with Sierpiński on the Hypothesis H), algebraic number theory, diophantine equations, analytical number theory and geometry of numbers. Volume II concludes with some papers from outside number theory, as well as a list of unsolved problems and unproved conjectures, taken from the work of Schinzel. Mathematics bicssc Number theory msc Field theory and polynomials msc Narkiewicz edt Urbanowicz edt https://ems.press/doi/10.4171/038-2 cover image https://content.ems.press/assets/public/images/books/cover-33.jpg nam a22 5a 4500 10.4171/037 DE-4084 2007-03-21 a fot 00| 0| cr nn mmmmamaa 070321e20070321gw fot 00| 0|eng d 9783037195376 10.4171/037 doi DE-4084 PBMP bicssc PBKJ bicssc 58J45 msc 81T20 msc 35L05 msc 35L15 msc 53C50 msc 81T05 msc Bär aut Wave Equations on Lorentzian Manifolds and Quantization. EMS Press 2007 1 online resource (202 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda ESI Lectures in Mathematics and Physics (esi) 3 2943-4939 Restricted to subscribers. https://ems.press/books This book provides a detailed introduction to linear wave equations on Lorentzian manifolds (for vector-bundle valued fields). After a collection of preliminary material in the first chapter one finds in the second chapter the construction of local fundamental solutions together with their Hadamard expansion. The third chapter establishes the existence and uniqueness of global fundamental solutions on globally hyperbolic spacetimes and discusses Green's operators and well-posedness of the Cauchy problem. The last chapter is devoted to field quantization in the sense of algebraic quantum field theory. The necessary basics on C\*-algebras and CCR-representations are developed in full detail. The text provides a self-contained introduction to these topics addressed to graduate students in mathematics and physics. At the same time it is intended as a reference for researchers in global analysis, general relativity, and quantum field theory. Differential & Riemannian geometry bicssc Differential calculus & equations bicssc Hyperbolic equations on manifolds msc Quantum field theory on curved space or space-time backgrounds msc Wave equation msc Initial value problems for second-order hyperbolic equations msc Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics msc Axiomatic quantum field theory; operator algebras msc Ginoux aut Pfäffle aut https://ems.press/doi/10.4171/037 cover image https://content.ems.press/assets/public/images/books/cover-34.png nam a22 5a 4500 10.4171/029 DE-4084 2007-05-25 a fot 00| 0| cr nn mmmmamaa 070525e20070525gw fot 00| 0|eng d 9783037195291 10.4171/029 doi DE-4084 PBKD bicssc 30-00 msc 32G15 msc 30F60 msc 30C62 msc 57N16 msc 53A35 msc 20F65 msc 30F20 msc 30F25 msc 30F10 msc 30F30 msc 30F40 msc 30F45 msc 14H15 msc 20H10 msc 30F15 msc 53B35 msc 57M07 msc 57M60 msc 14H60 msc 14D20 msc 20F38 msc Papadopoulos edt Handbook of Teichmüller Theory, Volume I. EMS Press 2007 1 online resource (802 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 11 2523-5141 Restricted to subscribers. https://ems.press/books The Teichmüller space of a surface was introduced by O. Teichmüller in the 1930s. It is a basic tool in the study of Riemann's moduli space and of the mapping class group. These objects are fundamental in several fields of mathematics including algebraic geometry, number theory, topology, geometry, and dynamics. The original setting of Teichmüller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry in the study of Teichmüller space and of its asymptotic geometry. Teichmüller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group G, most notably GPSL(2,) and GPSL(2,). In the 1980s, there evolved an essentially combinatorial treatment of the Teichmüller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmüller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmüller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are self-contained and have a pedagogical character. They are written by leading experts in the subject. Complex analysis, complex variables bicssc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functions of a complex variable msc Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) msc Teichmüller theory for Riemann surfaces msc Quasiconformal mappings in the complex plane msc Geometric structures on manifolds of high or arbitrary dimension msc Non-Euclidean differential geometry msc Geometric group theory msc Classification theory of Riemann surfaces msc Ideal boundary theory for Riemann surfaces msc Compact Riemann surfaces and uniformization msc Differentials on Riemann surfaces msc Kleinian groups (aspects of compact Riemann surfaces and uniformization) msc Conformal metrics (hyperbolic, Poincaré, distance functions) msc Families, moduli of curves (analytic) msc Fuchsian groups and their generalizations (group-theoretic aspects) msc Harmonic functions on Riemann surfaces msc Local differential geometry of Hermitian and Kählerian structures msc Topological methods in group theory msc Group actions on manifolds and cell complexes in low dimensions msc Vector bundles on curves and their moduli msc Algebraic moduli problems, moduli of vector bundles msc Other groups related to topology or analysis msc https://ems.press/doi/10.4171/029 cover image https://content.ems.press/assets/public/images/books/cover-35.png nam a22 5a 4500 10.4171/033 DE-4084 2007-05-31 a fot 00| 0| cr nn mmmmamaa 070531e20070531gw fot 00| 0|eng d 9783037195338 10.4171/033 doi DE-4084 PBKJ bicssc 35-02 msc 35K55 msc 35K65 msc Daskalopoulos aut Degenerate Diffusions ; Initial Value Problems and Local Regularity Theory. EMS Press 2007 1 online resource (207 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 1 2943-5005 Restricted to subscribers. https://ems.press/books The book deals with existence, uniqueness, regularity and asymptotic behavior of solutions to the initial value problem (Cauchy problem) and the initial-Dirichlet problem for a class of degenerate diffusions modeled on the porous medium type equation ut um, m 0, u 0. Such models arise in plasma physics, diffusions through porous media, thin liquid film dynamics as well as in geometric flows such as the Ricci flow on surfaces and the Yamabe flow. The approach presented to these problems is through the use of local regularity estimates and Harnack type inequalities, which yield compactness for families of solutions. The theory is quite complete in the slow diffusion case (m > 1) and in the supercritical fast diffusion case (mc < m < 1, mc (n - 2)+/n) while many problems remain in the range m mc. All of these aspects of the theory are discussed in the book. The book is addressed to both researchers and to graduate students with a good background in analysis and some previous exposure to partial differential equations. Differential calculus & equations bicssc Research exposition (monographs, survey articles) pertaining to partial differential equations msc Nonlinear parabolic equations msc Degenerate parabolic equations msc Kenig aut https://ems.press/doi/10.4171/033 cover image https://content.ems.press/assets/public/images/books/cover-36.png nam a22 5a 4500 10.4171/032 DE-4084 2007-05-31 a fot 00| 0| cr nn mmmmamaa 070531e20070531gw fot 00| 0|eng d 9783037195321 10.4171/032 doi DE-4084 PBP bicssc 22-02 msc 17B65 msc 22D05 msc 22E20 msc 22E65 msc 58B25 msc Hofmann aut The Lie Theory of Connected Pro-Lie Groups ; A Structure Theory for Pro-Lie Algebras, Pro-Lie Groups, and Connected Locally Compact Groups. EMS Press 2007 1 online resource (693 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 2 2943-5005 Restricted to subscribers. https://ems.press/books Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonné quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them. If a complete topological group G can be approximated by Lie groups in the sense that every identity neighborhood U of G contains a normal subgroup N such that G/N is a Lie group, then it is called a _pro-Lie group_. Every locally compact connected topological group and every compact group is a pro-Lie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of pro-Lie groups is. For half a century, locally compact pro-Lie groups have drifted through the literature, yet this is the first book which systematically treats the Lie and structure theory of pro-Lie groups irrespective of local compactness. This study fits very well into that current trend which addresses infinite dimensional Lie groups. The results of this text are based on a theory of pro-Lie algebras which parallels the structure theory of finite dimensional real Lie algebras to an astonishing degree even though it has to overcome greater technical obstacles. This book exposes a Lie theory of connected pro-Lie groups (and hence of connected locally compact groups) and illuminates the manifold ways in which their structure theory reduces to that of compact groups on the one hand and of finite dimensional Lie groups on the other. It is a continuation of the authors' fundamental monograph on the structure of compact groups (1998, 2006), and is an invaluable tool for researchers in topological groups, Lie theory, harmonic analysis and representation theory. It is written to be accessible to advanced graduate students wishing to study this fascinating and important area of current research, which has so many fruitful interactions with other fields of mathematics. The second edition is available [here](https://ems.press/books/etm/270). Topology bicssc Research exposition (monographs, survey articles) pertaining to topological groups msc Infinite-dimensional Lie (super)algebras msc General properties and structure of locally compact groups msc General properties and structure of other Lie groups msc Infinite-dimensional Lie groups and their Lie algebras: general properties msc Group structures and generalizations on infinite-dimensional manifolds msc Morris aut https://ems.press/doi/10.4171/032 cover image https://content.ems.press/assets/public/images/books/cover-37.png nam a22 5a 4500 10.4171/036 DE-4084 2007-05-24 a fot 00| 0| cr nn mmmmamaa 070524e20070524gw fot 00| 0|eng d 9783037195369 10.4171/036 doi DE-4084 PBMP bicssc 51F99 msc 53C23 msc 55M10 msc 54C20 msc 20F67 msc 20F69 msc Buyalo aut Elements of Asymptotic Geometry. EMS Press 2007 1 online resource (212 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Monographs in Mathematics (emm) 3 2523-5206 Restricted to subscribers. https://ems.press/books Asymptotic geometry is the study of metric spaces from a large scale point of view, where the local geometry does not come into play. An important class of model spaces are the hyperbolic spaces (in the sense of Gromov), for which the asymptotic geometry is nicely encoded in the boundary at infinity. In the first part of this book, in analogy with the concepts of classical hyperbolic geometry, the authors provide a systematic account of the basic theory of Gromov hyperbolic spaces. These spaces have been studied extensively in the last twenty years, and have found applications in group theory, geometric topology, Kleinian groups, as well as dynamics and rigidity theory. In the second part of the book, various aspects of the asymptotic geometry of arbitrary metric spaces are considered. It turns out that the boundary at infinity approach is not appropriate in the general case, but dimension theory proves useful for finding interesting results and applications. The text leads concisely to some central aspects of the theory. Each chapter concludes with a separate section containing supplementary results and bibliographical notes. Here the theory is also illustrated with numerous examples as well as relations to the neighboring fields of comparison geometry and geometric group theory. The book is based on lectures the authors presented at the Steklov Institute in St. Petersburg and the University of Zurich. It addressed to graduate students and researchers working in geometry, topology, and geometric group theory. Differential & Riemannian geometry bicssc Metric geometry msc Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces msc Dimension theory in algebraic topology msc Extension of maps msc Hyperbolic groups and nonpositively curved groups msc Asymptotic properties of groups msc Schroeder aut https://ems.press/doi/10.4171/036 cover image https://content.ems.press/assets/public/images/books/cover-38.png nam a22 5a 4500 10.4171/039 DE-4084 2007-08-06 a fot 00| 0| cr nn mmmmamaa 070806e20070806gw fot 00| 0|eng d 9783037195390 10.4171/039 doi DE-4084 PBK bicssc PBPD bicssc PBMW bicssc 19-02 msc 46-02 msc 46L80 msc 46A17 msc 46H30 msc 19D55 msc 19K35 msc Meyer aut Local and Analytic Cyclic Homology. EMS Press 2007 1 online resource (368 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 3 2943-5005 Restricted to subscribers. https://ems.press/books Periodic cyclic homology is a homology theory for non-commutative algebras that plays a similar role in non-commutative geometry as de Rham cohomology for smooth manifolds. While it produces good results for algebras of smooth or polynomial functions, it fails for bigger algebras such as most Banach algebras or C\*-algebras. Analytic and local cyclic homology are variants of periodic cyclic homology that work better for such algebras. In this book the author develops and compares these theories, emphasising their homological properties. This includes the excision theorem, invariance under passage to certain dense subalgebras, a Universal Coefficient Theorem that relates them to K-theory, and the Chern-Connes character for K-theory and K-homology. The cyclic homology theories studied in this text require a good deal of functional analysis in bornological vector spaces, which is supplied in the first chapters. The focal points here are the relationship with inductive systems and the functional calculus in non-commutative bornological algebras. The book is mainly intended for researchers and advanced graduate students interested in non-commutative geometry. Some chapters are more elementary and independent of the rest of the book, and will be of interest to researchers and students working in functional analysis and its applications. Calculus & mathematical analysis bicssc Algebraic topology bicssc Algebraic geometry bicssc Research exposition (monographs, survey articles) pertaining to \(K\)-theory msc Research exposition (monographs, survey articles) pertaining to functional analysis msc \(K\)-theory and operator algebras (including cyclic theory) msc Bornologies and related structures; Mackey convergence, etc. msc Functional calculus in topological algebras msc \(K\)-theory and homology; cyclic homology and cohomology msc Kasparov theory (\(KK\)-theory) msc https://ems.press/doi/10.4171/039 cover image https://content.ems.press/assets/public/images/books/cover-39.png nam a22 5a 4500 10.4171/035 DE-4084 2007-09-06 a fot 00| 0| cr nn mmmmamaa 070906e20070906gw fot 00| 0|eng d 9783037195352 10.4171/035 doi DE-4084 PBT bicssc 60G70 msc 60F99 msc 91B70 msc 62G32 msc 60G55 msc Balkema aut High Risk Scenarios and Extremes ; A geometric approach. EMS Press 2007 1 online resource (389 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 5 2943-4971 Restricted to subscribers. https://ems.press/books Quantitative Risk Management (QRM) has become a field of research of considerable importance to numerous areas of application, including insurance, banking, energy, medicine, reliability. Mainly motivated by examples from insurance and finance, the authors develop a theory for handling multivariate extremes. The approach borrows ideas from portfolio theory and aims at an intuitive approach in the spirit of the Peaks over Thresholds method. The point of view is geometric. It leads to a probabilistic description of what in QRM language may be referred to as a high risk scenario: the conditional behaviour of risk factors given that a large move on a linear combination (portfolio, say) has been observed. The theoretical models which describe such conditional extremal behaviour are characterized and their relation to the limit theory for coordinatewise maxima is explained. The first part is an elegant exposition of coordinatewise extreme value theory; the second half develops the more basic geometric theory. Besides a precise mathematical deduction of the main results, the text yields numerous discussions of a more applied nature. A twenty page preview introduces the key concepts; the extensive introduction provides links to financial mathematics and insurance theory. The book is based on a graduate course on point processes and extremes. It could form the basis for an advanced course on multivariate extreme value theory or a course on mathematical issues underlying risk. Students in statistics and finance with a mathematical, quantitative background are the prime audience. Actuaries and risk managers involved in data based risk analysis will find the models discussed in the book stimulating. The text contains many indications for further research. Probability & statistics bicssc Extreme value theory; extremal stochastic processes msc Limit theorems in probability theory msc Stochastic models in economics msc Statistics of extreme values; tail inference msc Point processes (e.g., Poisson, Cox, Hawkes processes) msc Embrechts aut https://ems.press/doi/10.4171/035 cover image https://content.ems.press/assets/public/images/books/cover-41.png nam a22 5a 4500 10.4171/040 DE-4084 2007-11-21 a fot 00| 0| cr nn mmmmamaa 071121e20071121gw fot 00| 0|eng d 9783037195406 10.4171/040 doi DE-4084 PBKJ bicssc 35-02 msc 35J25 msc 35S15 msc Harutyunyan aut Elliptic Mixed, Transmission and Singular Crack Problems. EMS Press 2007 1 online resource (777 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 4 2943-5005 Restricted to subscribers. https://ems.press/books Mixed, transmission, or crack problems belong to the analysis of boundary value problems on manifolds with singularities. The Zaremba problem with a jump between Dirichlet and Neumann conditions along an interface on the boundary is a classical example. The central theme of this book is to study mixed problems in standard Sobolev spaces as well as in weighted edge spaces where the interfaces are interpreted as edges. Parametrices and regularity of solutions are obtained within a systematic calculus of boundary value problems on manifolds with conical or edge singularities. This calculus allows singularities on the interface, and homotopies between mixed and crack problems. Additional edge conditions are computed in terms of relative index results. In a detailed final chapter, the intuitive ideas of the approach are illustrated, and there is a discussion of future challenges. A special feature of the text is the inclusion of many worked out examples which help the reader to appreciate the scope of the theory and to treat new cases of practical interest. This book is addressed to mathematicians and physicists interested in models with singularities, associated boundary value problems, and their solvability strategies based on pseudo-differential operators. The material is also useful for students in higher semesters and young researchers, as well as for experienced specialists working in analysis on manifolds with geometric singularities, the applications of index theory and spectral theory, operator algebras with symbolic structures, quantisation, and asymptotic analysis. Differential calculus & equations bicssc Research exposition (monographs, survey articles) pertaining to partial differential equations msc Boundary value problems for second-order elliptic equations msc Boundary value problems for PDEs with pseudodifferential operators msc Schulze aut https://ems.press/doi/10.4171/040 cover image https://content.ems.press/assets/public/images/books/cover-40.png nam a22 5a 4500 10.4171/042 DE-4084 2007-11-21 a fot 00| 0| cr nn mmmmamaa 071121e20071121gw fot 00| 0|eng d 9783037195420 10.4171/042 doi DE-4084 PBKJ bicssc 35-01 msc 46-01 msc 35J25 msc 35P15 msc 42B35 msc 46E35 msc 46F05 msc 47B06 msc 47F05 msc Haroske aut Distributions, Sobolev Spaces, Elliptic Equations. EMS Press 2007 1 online resource (303 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 3 2943-4955 Restricted to subscribers. https://ems.press/books It is the main aim of this book to develop at an accessible, moderate level an L2 theory for elliptic differential operators of second order on bounded smooth domains in Euclidean n\-space, including a priori estimates for boundary-value problems in terms of (fractional) Sobolev spaces on domains and on their boundaries, together with a related spectral theory. The presentation is preceded by an introduction to the classical theory for the Laplace-Poisson equation, and some chapters providing required ingredients such as the theory of distributions, Sobolev spaces and the spectral theory in Hilbert spaces. The book grew out of two-semester courses the authors have given several times over a period of ten years at the Friedrich Schiller University of Jena. It is addressed to graduate students and mathematicians who have a working knowledge of calculus, measure theory and the basic elements of functional analysis (as usually covered by undergraduate courses) and who are seeking an accessible introduction to some aspects of the theory of function spaces and its applications to elliptic equations. Differential calculus & equations bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis msc Boundary value problems for second-order elliptic equations msc Estimates of eigenvalues in context of PDEs msc Function spaces arising in harmonic analysis msc Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems msc Topological linear spaces of test functions, distributions and ultradistributions msc Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators msc General theory of partial differential operators msc Triebel aut https://ems.press/doi/10.4171/042 cover image https://content.ems.press/assets/public/images/books/cover-42.png nam a22 5a 4500 10.4171/044 DE-4084 2008-02-12 a fot 00| 0| cr nn mmmmamaa 080212e20080212gw fot 00| 0|eng d 9783037195444 10.4171/044 doi DE-4084 PBKQ bicssc 28A75 msc 26B15 msc 49Q15 msc 49Q20 msc De Lellis aut Rectifiable Sets, Densities, and Tangent Measures. EMS Press 2008 1 online resource (133 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 7 2943-4971 Restricted to subscribers. https://ems.press/books The characterization of rectifiable sets through the existence of densities is a pearl of geometric measure theory. The difficult proof, due to Preiss, relies on many beautiful and deep ideas and novel techniques. Some of them have already proven useful in other contexts, whereas others have not yet been exploited. These notes give a simple and short presentation of the former, and provide some perspective of the latter. This text emerged from a course on rectifiability given at the University of Zürich. It is addressed both to researchers and students, the only prerequisite is a solid knowledge in standard measure theory. The first four chapters give an introduction to rectifiable sets and measures in euclidean spaces, covering classical topics such as the area formula, the theorem of Marstrand and the most elementary rectifiability criterions. The fifth chapter is dedicated to a subtle rectifiability criterion due to Marstrand and generalized by Mattila, and the last three focus on Preiss' result. The aim is to provide a self-contained reference for anyone interested in an overview of this fascinating topic. Calculus of variations bicssc Length, area, volume, other geometric measure theory msc Integration of real functions of several variables: length, area, volume msc Geometric measure and integration theory, integral and normal currents in optimization msc Variational problems in a geometric measure-theoretic setting msc https://ems.press/doi/10.4171/044 cover image https://content.ems.press/assets/public/images/books/cover-43.jpg nam a22 5a 4500 10.4171/043 DE-4084 2008-02-28 a fot 00| 0| cr nn mmmmamaa 080228e20080228gw fot 00| 0|eng d 9783037195437 10.4171/043 doi DE-4084 PBF bicssc PB bicssc 46-01 msc 46L55 msc 22A22 msc 22D25 msc 22D35 msc 46L10 msc Timmermann aut An Invitation to Quantum Groups and Duality ; From Hopf Algebras to Multiplicative Unitaries and Beyond. EMS Press 2008 1 online resource (427 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 4 2943-4955 Restricted to subscribers. https://ems.press/books This book provides an introduction to the theory of quantum groups with emphasis on their duality and on the setting of operator algebras. Part I of the text presents the basic theory of Hopf algebras, Van Daeles duality theory of algebraic quantum groups, and Woronowiczs compact quantum groups, staying in a purely algebraic setting. Part II focuses on quantum groups in the setting of operator algebras. Woronowiczs compact quantum groups are treated in the setting of C\*-algebras, and the fundamental multiplicative unitaries of Baaj and Skandalis are studied in detail. An outline of Kustermans and Vaes comprehensive theory of locally compact quantum groups completes this part. Part III leads to selected topics, such as coactions, Baaj-Skandalis-duality, and approaches to quantum groupoids in the setting of operator algebras. The book is addressed to graduate students and non-experts from other fields. Only basic knowledge of (multi-) linear algebra is required for the first part, while the second and third part assume some familiarity with Hilbert spaces, C\*-algebras, and von Neumann algebras. Algebra bicssc Mathematics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis msc Noncommutative dynamical systems msc Topological groupoids (including differentiable and Lie groupoids) msc \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations msc Duality theorems for locally compact groups msc General theory of von Neumann algebras msc https://ems.press/doi/10.4171/043 cover image https://content.ems.press/assets/public/images/books/cover-44.png nam a22 5a 4500 10.4171/041 DE-4084 2008-02-29 a fot 00| 0| cr nn mmmmamaa 080229e20080229gw fot 00| 0|eng d 9783037195413 10.4171/041 doi DE-4084 PBG bicssc PB bicssc 20-01 msc 20D08 msc 20E05 msc 20E06 msc 20E08 msc 20F28 msc Bogopolski aut Introduction to Group Theory. EMS Press 2008 1 online resource (187 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 5 2943-4955 Restricted to subscribers. https://ems.press/books This book quickly introduces beginners to general group theory and then focuses on three main themes: * finite group theory, including sporadic groups; * combinatorial and geometric group theory, including the Bass-Serre theory of groups acting on trees; * the theory of train tracks by Bestvina and Handel for automorphisms of free groups. With its many examples, exercises, and full solutions to selected exercises, this text provides a gentle introduction that is ideal for self-study and an excellent preparation for applications. A distinguished feature of the presentation is that algebraic and geometric techniques are balanced. The beautiful theory of train tracks is illustrated by two nontrivial examples. Presupposing only a basic knowledge of algebra, the book is addressed to anyone interested in group theory: from advanced undergraduate and graduate students to specialists. Groups & group theory bicssc Mathematics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory msc Simple groups: sporadic groups msc Free nonabelian groups msc Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations msc Groups acting on trees msc Automorphism groups of groups msc https://ems.press/doi/10.4171/041 cover image https://content.ems.press/assets/public/images/books/cover-45.png nam a22 5a 4500 10.4171/049 DE-4084 2008-03-03 a fot 00| 0| cr nn mmmmamaa 080303e20080303gw fot 00| 0|eng d 9783037195499 10.4171/049 doi DE-4084 PBKD bicssc PBK bicssc 32-01 msc 32A05 msc 32A10 msc 32D05 msc 32E05 msc 32F45 msc Jarnicki aut First Steps in Several Complex Variables: Reinhardt Domains. EMS Press 2008 1 online resource (367 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 6 2943-4955 Restricted to subscribers. https://ems.press/books This book provides a comprehensive introduction to the field of several complex variables in the setting of a very special but basic class of domains, the so-called Reinhardt domains. In this way the reader may learn much about this area without encountering too many technical difficulties. Chapter 1 describes the fundamental notions and the phenomenon of simultaneous holomorphic extension. Chapter 2 presents a fairly complete discussion of biholomorphisms of bounded (complete) Reinhardt domains in the two dimensional case. The third chapter gives a classification of Reinhardt domains of existence for the most important classes of holomorphic functions. The last chapter deals with invariant functions and gives explicit calculations of many of them on certain Reinhardt domains. Numerous exercises are included to help the readers with their understanding of the material. Further results and open problems are added which may be useful as seminar topics. The primary aim of this book is to introduce students or non-experts to some of the main research areas in several complex variables. The book provides a friendly invitation to this field as the only prerequisite is a basic knowledge of analysis. Complex analysis, complex variables bicssc Calculus & mathematical analysis bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces msc Power series, series of functions of several complex variables msc Holomorphic functions of several complex variables msc Domains of holomorphy msc Holomorphically convex complex spaces, reduction theory msc Invariant metrics and pseudodistances in several complex variables msc Pflug aut https://ems.press/doi/10.4171/049 cover image https://content.ems.press/assets/public/images/books/cover-46.png nam a22 5a 4500 10.4171/050 DE-4084 2008-04-08 a fot 00| 0| cr nn mmmmamaa 080408e20080408gw fot 00| 0|eng d 9783037195505 10.4171/050 doi DE-4084 PBMP bicssc PB bicssc 53-01 msc 20C05 msc 20G20 msc 37J35 msc 53A10 msc 53D05 msc 53D17 msc 57S17 msc 58A05 msc Taimanov aut Lectures on Differential Geometry. EMS Press 2008 1 online resource (219 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 7 2523-5184 Restricted to subscribers. https://ems.press/books Differential geometry studies geometrical objects using analytical methods. Like modern analysis itself, differential geometry originates in classical mechanics. For instance, geodesics and minimal surfaces are defined via variational principles and the curvature of a curve is easily interpreted as the acceleration with respect to the path length parameter. Modern differential geometry in its turn strongly contributed to modern physics. This book gives an introduction to the basics of differential geometry, keeping in mind the natural origin of many geometrical quantities, as well as the applications of differential geometry and its methods to other sciences. The text is divided into three parts. The first part covers the basics of curves and surfaces, while the second part is designed as an introduction to smooth manifolds and Riemannian geometry. In particular, Chapter 5 contains short introductions to hyperbolic geometry and geometrical principles of special relativity theory. Here, only a basic knowledge of algebra, calculus and ordinary differential equations is required. The third part is more advanced and introduces into matrix Lie groups and Lie algebras, representation theory of groups, symplectic and Poisson geometry, and applications of complex analysis in surface theory. The book is based on lectures the author held repeatedly at Novosibirsk State University. It is addressed to students as well as to anyone who wants to learn the basics of differential geometry. Differential & Riemannian geometry bicssc Mathematics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry msc Group rings of finite groups and their modules (group-theoretic aspects) msc Linear algebraic groups over the reals, the complexes, the quaternions msc Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests msc Minimal surfaces in differential geometry, surfaces with prescribed mean curvature msc Symplectic manifolds (general theory) msc Poisson manifolds; Poisson groupoids and algebroids msc Finite transformation groups msc Differentiable manifolds, foundations msc https://ems.press/doi/10.4171/050 cover image https://content.ems.press/assets/public/images/books/cover-47.png nam a22 5a 4500 10.4171/045 DE-4084 2008-04-29 a fot 00| 0| cr nn mmmmamaa 080429e20080429gw fot 00| 0|eng d 9783037195451 10.4171/045 doi DE-4084 PBT bicssc 60-02 msc 60B15 msc 62E10 msc 43A05 msc 43A25 msc 43A35 msc 39B52 msc Feldman aut Functional Equations and Characterization Problems on Locally Compact Abelian Groups. EMS Press 2008 1 online resource (268 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 5 2943-5005 Restricted to subscribers. https://ems.press/books This book deals with the characterization of probability distributions. It is well known that both the sum and the difference of two Gaussian independent random variables with equal variance are independent as well. The converse statement was proved independently by M. Kac and S. N. Bernstein. This result is a famous example of a characterization theorem. In general, characterization problems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions in these variables. In recent years, a great deal of attention has been focused upon generalizing the classical characterization theorems to random variables with values in various algebraic structures such as locally compact Abelian groups, Lie groups, quantum groups, or symmetric spaces. The present book is aimed at the generalization of some well-known characterization theorems to the case of independent random variables taking values in a locally compact Abelian group X. The main attention is paid to the characterization of the Gaussian and the idempotent distribution (group analogs of the Kac-Bernstein, Skitovich-Darmois, and Heyde theorems). The solution of the corresponding problems is reduced to the solution of some functional equations in the class of continuous positive definite functions defined on the character group of X. Group analogs of the Cramér and Marcinkiewicz theorems are also studied. The author is an expert in algebraic probability theory. His comprehensive and self-contained monograph is addressed to mathematicians working in probability theory on algebraic structures, abstract harmonic analysis, and functional equations. The book concludes with comments and unsolved problems that provide further stimulation for future research in the theory. Probability & statistics bicssc Research exposition (monographs, survey articles) pertaining to probability theory msc Probability measures on groups or semigroups, Fourier transforms, factorization msc Characterization and structure theory of statistical distributions msc Measures on groups and semigroups, etc. msc Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups msc Positive definite functions on groups, semigroups, etc. msc Functional equations for functions with more general domains and/or ranges msc https://ems.press/doi/10.4171/045 cover image https://content.ems.press/assets/public/images/books/cover-48.png nam a22 5a 4500 10.4171/054 DE-4084 2008-08-19 a fot 00| 0| cr nn mmmmamaa 080819e20080819gw fot 00| 0|eng d 9783037195543 10.4171/054 doi DE-4084 PBPH bicssc TGB bicssc PB bicssc 58E05 msc 57R70 msc 57R30 msc Farber aut Invitation to Topological Robotics. EMS Press 2008 1 online resource (143 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 10 2943-4971 Restricted to subscribers. https://ems.press/books The book discusses several selected topics of a new emerging area of research lying on the interface between topology and engineering. The first main topic of the book is topology of configuration spaces of mechanical linkages. These manifolds arise in various fields of mathematics and in other sciences, e.g. engineering, statistics, molecular biology. To compute Betti numbers of these configuration spaces we apply a new technique of Morse theory in the presence of an involution. A significant result of topology of linkages presented in the book is a solution of a conjecture of Kevin Walker which states that the relative sizes of bars of a linkage are determined, up to certain equivalence, by the cohomology algebra of the linkage configuration space. The book also describes a new probabilistic approach to topology of linkages which treats the bar lengths as random variables and studies mathematical expectations of Betti numbers. The second main topic of the book is topology of configuration spaces associated to polyhedra. The book gives an account of a beautiful work of S.R. Gal suggesting an explicit formula for the generating function encoding Euler characteristics of these spaces. Next we study the knot theory of a robot arm focusing on a recent important result of R. Connelly, E. Demain and G. Rote. Finally, the book investigates topological problems arising in the theory of robot motion planning algorithms and studies the homotopy invariant **TC**(_X_) measuring navigational complexity of configuration spaces. The book is intended as an appetizer and will introduce the reader to many fascinating topological problems motivated by engineering. Analytic topology bicssc Mechanical engineering bicssc Mathematics bicssc Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces msc Critical points and critical submanifolds in differential topology msc Foliations in differential topology; geometric theory msc https://ems.press/doi/10.4171/054 cover image https://content.ems.press/assets/public/images/books/cover-49.jpg nam a22 5a 4500 10.4171/052 DE-4084 2008-09-01 a fot 00| 0| cr nn mmmmamaa 080901e20080901gw fot 00| 0|eng d 9783037195529 10.4171/052 doi DE-4084 PBM bicssc PB bicssc 52C07 msc 52B20 msc 05A15 msc 52B45 msc 52B55 msc 52C45 msc 11H06 msc Barvinok aut Integer Points in Polyhedra. EMS Press 2008 1 online resource (199 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 11 2943-4971 Restricted to subscribers. https://ems.press/books This is a self-contained exposition of several core aspects of the theory of rational polyhedra with a view towards algorithmic applications to efficient counting of integer points, a problem arising in many areas of pure and applied mathematics. The approach is based on the consistent development and application of the apparatus of generating functions and the algebra of polyhedra. Topics range from classical, such as the Euler characteristic, continued fractions, Ehrhart polynomial, Minkowski Convex Body Theorem, and the Lenstra- Lenstra-Lovász lattice reduction algorithm, to recent advances such as the Berline-Vergne local formula. The text is intended for graduate students and researchers. Prerequisites are a modest background in linear algebra and analysis as well as some general mathematical maturity. Numerous figures, exercises of varying degree of difficulty as well as references to the literature and publicly available software make the text suitable for a graduate course. Geometry bicssc Mathematics bicssc Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry) msc Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) msc Exact enumeration problems, generating functions msc Dissections and valuations (Hilbert's third problem, etc.) msc Computational aspects related to convexity msc Combinatorial complexity of geometric structures msc Lattices and convex bodies (number-theoretic aspects) msc https://ems.press/doi/10.4171/052 cover image https://content.ems.press/assets/public/images/books/cover-50.jpg nam a22 5a 4500 10.4171/047 DE-4084 2008-06-11 a fot 00| 0| cr nn mmmmamaa 080611e20080611gw fot 00| 0|eng d 9783037195475 10.4171/047 doi DE-4084 PHU bicssc PBW bicssc PB bicssc 81R50 msc 81R12 msc Enriquez edt Quantum Groups. EMS Press 2008 1 online resource (140 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 12 2523-5141 Restricted to subscribers. https://ems.press/books The volume starts with a lecture course by P. Etingof on tensor categories (notes by D. Calaque). This course is an introduction to tensor categories, leading to topics of recent research such as realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory, categorical dimensions, Frobenius-Perron dimensions, and the classification of tensor categories. The remainder of the book consists of three detailed expositions on associators and the Vassiliev invariants of knots, classical and quantum integrable systems and elliptic algebras, and the groups of algebra automorphisms of quantum groups. The preface sets the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of the ongoing research in the domain of quantum groups, an important subject of current mathematical physics. Mathematical physics bicssc Applied mathematics bicssc Mathematics bicssc Quantum groups and related algebraic methods applied to problems in quantum theory msc Groups and algebras in quantum theory and relations with integrable systems msc https://ems.press/doi/10.4171/047 cover image https://content.ems.press/assets/public/images/books/cover-51.png nam a22 5a 4500 10.4171/051 DE-4084 2008-06-11 a fot 00| 0| cr nn mmmmamaa 080611e20080611gw fot 00| 0|eng d 9783037195512 10.4171/051 doi DE-4084 PBMP bicssc 53-00 msc 53C50 msc Alekseevsky edt Recent Developments in Pseudo-Riemannian Geometry. EMS Press 2008 1 online resource (549 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda ESI Lectures in Mathematics and Physics (esi) 4 2943-4939 Restricted to subscribers. https://ems.press/books This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the field. Topics covered are: * Classification of pseudo-Riemannian symmetric spaces * Holonomy groups of Lorentzian and pseudo-Riemannian manifolds * Hypersymplectic manifolds * Anti-self-dual conformal structures in neutral signature and integrable systems * Neutral Kähler surfaces and geometric optics * Geometry and dynamics of the Einstein universe * Essential conformal structures and conformal transformations in pseudo-Riemannian geometry * The causal hierarchy of spacetimes * Geodesics in pseudo-Riemannian manifolds * Lorentzian symmetric spaces in supergravity * Generalized geometries in supergravity * Einstein metrics with Killing leaves The book is addressed to advanced students as well as to researchers in differential geometry, global analysis, general relativity and string theory. It shows essential differences between the geometry on manifolds with positive definite metrics and on those with indefinite metrics, and highlights the interesting new geometric phenomena, which naturally arise in the indefinite metric case. The reader finds a description of the present state of art in the field as well as open problems, which can stimulate further research. Differential & Riemannian geometry bicssc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to differential geometry msc Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics msc Baum edt https://ems.press/doi/10.4171/051 cover image https://content.ems.press/assets/public/images/books/cover-53.png nam a22 5a 4500 10.4171/018 DE-4084 2008-06-26 a fot 00| 0| cr nn mmmmamaa 080626e20080626gw fot 00| 0|eng d 9783037195185 10.4171/018 doi DE-4084 PB bicssc PBK bicssc 42-01 msc 42C40 msc 65T60 msc Mohlenkamp aut Wavelets, Their Friends, and What They Can Do for You. EMS Press 2008 1 online resource (119 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 8 2523-5184 Restricted to subscribers. https://ems.press/books So what is all the fuss about wavelets? You can find out by reading these notes. They will introduce you to the central concepts surrounding wavelets and their applications. By focusing on the essential ideas and arguments, they enable you to get to the heart of the matter as quickly as possible. They then point you to the appropriate places in the literature for detailed proofs and real applications, so you can continue your study. They begin with the notion of time-frequency analysis, present the multiresolution analysis and basic wavelet construction, introduce you to the many friends, relatives and mutations of wavelets, and finally give a selection of applications. They are suitable for beginning graduate students and above. A preliminary chapter containing some of the prerequisite concepts and definitions is included for reference. Mathematics bicssc Calculus & mathematical analysis bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces msc Nontrigonometric harmonic analysis involving wavelets and other special systems msc Numerical methods for wavelets msc Pereyra aut https://ems.press/doi/10.4171/018 cover image https://content.ems.press/assets/public/images/books/cover-54.png nam a22 5a 4500 10.4171/065 DE-4084 2008-07-04 a fot 00| 0| cr nn mmmmamaa 080704e20080704gw fot 00| 0|eng d 9783037195659 10.4171/065 doi DE-4084 PBMW bicssc 14L24 msc 14H60 msc 13A50 msc 14D20 msc 14L30 msc Schmitt aut Geometric Invariant Theory and Decorated Principal Bundles. EMS Press 2008 1 online resource (396 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 9 2943-4971 Restricted to subscribers. https://ems.press/books The book starts with an introduction to Geometric Invariant Theory (GIT). The fundamental results of Hilbert and Mumford are exposed as well as more recent topics such as the instability flag, the finiteness of the number of quotients, and the variation of quotients. In the second part, GIT is applied to solve the classification problem of decorated principal bundles on a compact Riemann surface. The solution is a quasi-projective moduli scheme which parameterizes those objects that satisfy a semistability condition originating from gauge theory. The moduli space is equipped with a generalized Hitchin map. Via the universal Kobayashi-Hitchin correspondence, these moduli spaces are related to moduli spaces of solutions of certain vortex type equations. Potential applications include the study of representation spaces of the fundamental group of compact Riemann surfaces. The book concludes with a brief discussion of generalizations of these findings to higher dimensional base varieties, positive characteristic, and parabolic bundles. The text is fairly self-contained (e.g., the necessary background from the theory of principal bundles is included) and features numerous examples and exercises. It addresses students and researchers with a working knowledge of elementary algebraic geometry. Algebraic geometry bicssc Geometric invariant theory msc Vector bundles on curves and their moduli msc Actions of groups on commutative rings; invariant theory msc Algebraic moduli problems, moduli of vector bundles msc Group actions on varieties or schemes (quotients) msc https://ems.press/doi/10.4171/065 cover image https://content.ems.press/assets/public/images/books/cover-224.jpg nam a22 5a 4500 10.4171/019 DE-4084 2008-09-02 a fot 00| 0| cr nn mmmmamaa 080902e20080902gw fot 00| 0|eng d 9783037195192 10.4171/019 doi DE-4084 PBKF bicssc PB bicssc 46-02 msc 46E35 msc 42C40 msc 42B35 msc 28A80 msc Triebel aut Function Spaces and Wavelets on Domains. EMS Press 2008 1 online resource (265 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 7 2943-5005 Restricted to subscribers. https://ems.press/books Wavelets have emerged as an important tool in analyzing functions containing discontinuities and sharp spikes. They were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Interchanges between these fields during the last ten years have led to many new wavelet applications such as image compression, turbulence, human vision, radar, earthquake prediction, and pure mathematics applications such as solving partial differential equations. This book develops a theory of wavelet bases and wavelet frames for function spaces on various types of domains. Starting with the usual spaces on Euclidean spaces and their periodic counterparts, the exposition moves on to so-called thick domains (including Lipschitz domains and snowflake domains). Especially, wavelet expansions and extensions to corresponding spaces on Euclidean n\-spaces are developed. Finally, spaces on smooth and cellular domains and related manifolds are treated. Although the presentation relies on the recent theory of function spaces, basic notation and classical results are repeated in order to make the text self-contained. The book is addressed to two types of readers: researchers in the theory of function spaces who are interested in wavelets as new effective building blocks for functions, and scientists who wish to use wavelet bases in classical function spaces for various applications. Adapted to the second type of readers, the preface contains a guide to where one finds basic definitions and key assertions. Functional analysis & transforms bicssc Mathematics bicssc Research exposition (monographs, survey articles) pertaining to functional analysis msc Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems msc Nontrigonometric harmonic analysis involving wavelets and other special systems msc Function spaces arising in harmonic analysis msc Fractals msc https://ems.press/doi/10.4171/019 cover image https://content.ems.press/assets/public/images/books/cover-58.png nam a22 5a 4500 10.4171/026 DE-4084 2008-09-02 a fot 00| 0| cr nn mmmmamaa 080902e20080902gw fot 00| 0|eng d 9783037195260 10.4171/026 doi DE-4084 PBKS bicssc PB bicssc 65-02 msc 65Y20 msc 68Q17 msc 68Q25 msc 41A63 msc 46E22 msc 28C20 msc 46E30 msc Novak aut Tractability of Multivariate Problems. Volume I. Linear Information EMS Press 2008 1 online resource (395 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 6 2943-5005 Restricted to subscribers. https://ems.press/books Multivariate problems occur in many applications. These problems are defined on spaces of d\-variate functions and d can be huge - in the hundreds or even in the thousands. Some high-dimensional problems can be solved efficiently to within , i.e., the cost increases polynomially in 1 and d. However, there are many multivariate problems for which even the minimal cost increases exponentially in d. This exponential dependence on d is called _intractability_ or the _curse of dimensionality_. This is the first of a three-volume set comprising a comprehensive study of the tractability of multivariate problems. It is devoted to algorithms using linear information consisting of arbitrary linear functionals. The theory for multivariate problems is developed in various settings: worst case, average case, randomized and probabilistic. A problem is tractable if its minimal cost is _not_ exponential in 1 and d. There are various notions of tractability, depending on how we measure the lack of exponential dependence. For example, a problem is polynomially tractable if its minimal cost is polynomial in 1 and d. The study of tractability was initiated about 15 years ago. This is the first research monograph on this subject. Many multivariate problems suffer from the curse of dimensionality when they are defined over classical (unweighted) spaces. But many practically important problems are solved today for huge d in a reasonable time. One of the most intriguing challenges of theory is to understand why this is possible. Multivariate problems may become tractable if they are defined over _weighted_ spaces with properly decaying weights. In this case, all variables and groups of variables are moderated by weights. The main purpose of this book is to study weighted spaces and to obtain conditions on the weights that are necessary and sufficient to achieve various notions of tractability. The book is of interest for researchers working in computational mathematics, especially in approximation of high-dimensional problems. It may be also suitable for graduate courses and seminars. The text concludes with a list of thirty open problems that can be good candidates for future tractability research. Numerical analysis bicssc Mathematics bicssc Research exposition (monographs, survey articles) pertaining to numerical analysis msc Complexity and performance of numerical algorithms msc Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) msc Analysis of algorithms and problem complexity msc Multidimensional problems msc Hilbert spaces with reproducing kernels ( (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) msc Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) msc Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) msc Woźniakowski aut https://ems.press/doi/10.4171/026 cover image https://content.ems.press/assets/public/images/books/cover-56.png nam a22 5a 4500 10.4171/048 DE-4084 2008-09-01 a fot 00| 0| cr nn mmmmamaa 080901e20080901gw fot 00| 0|eng d 9783037195482 10.4171/048 doi DE-4084 PBPD bicssc 55-01 msc 57-01 msc tom Dieck aut Algebraic Topology ; Corrected 2nd printing, 2010. EMS Press 2008 1 online resource (578 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 7 2943-4955 Restricted to subscribers. https://ems.press/books This book is written as a textbook on algebraic topology. The first part covers the material for two introductory courses about homotopy and homology. The second part presents more advanced applications and concepts (duality, characteristic classes, homotopy groups of spheres, bordism). The author recommends to start an introductory course with homotopy theory. For this purpose, classical results are presented with new elementary proofs. Alternatively, one could start more traditionally with singular and axiomatic homology. Additional chapters are devoted to the geometry of manifolds, cell complexes and fibre bundles. A special feature is the rich supply of nearly 500 exercises and problems. Several sections include topics which have not appeared before in textbooks as well as simplified proofs for some important results. Prerequisites are standard point set topology (as recalled in the first chapter), elementary algebraic notions (modules, tensor product), and some terminology from category theory. The aim of the book is to introduce advanced undergraduate and graduate (masters) students to basic tools, concepts and results of algebraic topology. Sufficient background material from geometry and algebra is included. Algebraic topology bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes msc https://ems.press/doi/10.4171/048 cover image https://content.ems.press/assets/public/images/books/cover-57.png nam a22 5a 4500 10.4171/067 DE-4084 2008-09-24 a fot 00| 0| cr nn mmmmamaa 080924e20080924gw fot 00| 0|eng d 9783037195673 10.4171/067 doi DE-4084 PBK bicssc PB bicssc 65M70 msc 65Z05 msc 81-08 msc Lubich aut From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis. EMS Press 2008 1 online resource (153 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 12 2943-4971 Restricted to subscribers. https://ems.press/books Quantum dynamics of molecules poses a variety of computational challenges that are presently at the forefront of research efforts in numerical analysis in a number of application areas: high-dimensional partial differential equations, multiple scales, highly oscillatory solutions, and geometric structures such as symplecticity and reversibility that are favourably preserved in discretizations. This text addresses such problems in quantum mechanics from the viewpoint of numerical analysis, illustrating them to a large extent on intermediate models between the Schrödinger equation of full many-body quantum dynamics and the Newtonian equations of classical molecular dynamics. The fruitful interplay between quantum dynamics and numerical analysis is emphasized. Calculus & mathematical analysis bicssc Mathematics bicssc Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs msc Applications to the sciences msc Computational methods for problems pertaining to quantum theory msc https://ems.press/doi/10.4171/067 cover image https://content.ems.press/assets/public/images/books/cover-55.jpg nam a22 5a 4500 10.4171/062 DE-4084 2008-09-24 a fot 00| 0| cr nn mmmmamaa 080924e20080924gw fot 00| 0|eng d 9783037195628 10.4171/062 doi DE-4084 PBF bicssc PB bicssc 16Gxx msc 03Cxx msc 05Exx msc 13Axx msc 13Cxx msc 13Hxx msc 14Dxx msc 14Gxx msc 14Lxx msc 14Mxx msc 16Dxx msc 16Exx msc 16Sxx msc 17Bxx msc 18Exx msc 18Gxx msc 20Cxx msc 20Gxx msc 20Jxx msc 32Sxx msc 55Pxx msc 57Mxx msc 81Rxx msc Skowroński edt Trends in Representation Theory of Algebras and Related Topics. EMS Press 2008 1 online resource (722 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 1 2523-5168 Restricted to subscribers. https://ems.press/books This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincaré duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, model theory. The book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field. Algebra bicssc Mathematics bicssc Representation theory of associative rings and algebras msc Model theory msc Algebraic combinatorics msc General commutative ring theory msc Theory of modules and ideals in commutative rings msc Local rings and semilocal rings msc Families, fibrations in algebraic geometry msc Arithmetic problems in algebraic geometry; Diophantine geometry msc Algebraic groups msc Special varieties msc Modules, bimodules and ideals in associative algebras msc Homological methods in associative algebras msc Associative rings and algebras arising under various constructions msc Lie algebras and Lie superalgebras msc Categorical algebra msc Homological algebra in category theory, derived categories and functors msc Representation theory of groups msc Linear algebraic groups and related topics msc Connections of group theory with homological algebra and category theory msc Complex singularities msc Homotopy theory msc General low-dimensional topology msc Groups and algebras in quantum theory msc https://ems.press/doi/10.4171/062 cover image https://content.ems.press/assets/public/images/books/cover-59.png nam a22 5a 4500 10.4171/060 DE-4084 2008-10-06 a fot 00| 0| cr nn mmmmamaa 081006e20081006gw fot 00| 0|eng d 9783037195604 10.4171/060 doi DE-4084 PBMW bicssc 19-06 msc 58-06 msc 14A22 msc 14Fxx msc 46Lxx msc 53D55 msc 58Bxx msc Cortiñas edt K-Theory and Noncommutative Geometry. EMS Press 2008 1 online resource (454 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 2 2523-5168 Restricted to subscribers. https://ems.press/books Since its inception 50 years ago, K-theory has been a tool for understanding a wide-ranging family of mathematical structures and their invariants: topological spaces, rings, algebraic varieties and operator algebras are the dominant examples. The invariants range from characteristic classes in cohomology, determinants of matrices, Chow groups of varieties, as well as traces and indices of elliptic operators. Thus K-theory is notable for its connections with other branches of mathematics. Noncommutative geometry develops tools which allow one to think of noncommutative algebras in the same footing as commutative ones: as algebras of functions on (noncommutative) spaces. The algebras in question come from problems in various areas of mathematics and mathematical physics; typical examples include algebras of pseudodifferential operators, group algebras, and other algebras arising from quantum field theory. To study noncommutative geometric problems one considers invariants of the relevant noncommutative algebras. These invariants include algebraic and topological K-theory, and also cyclic homology, discovered independently by Alain Connes and Boris Tsygan, which can be regarded both as a noncommutative version of de Rham cohomology and as an additive version of K-theory. There are primary and secondary Chern characters which pass from K-theory to cyclic homology. These characters are relevant both to noncommutative and commutative problems, and have applications ranging from index theorems to the detection of singularities of commutative algebraic varieties. The contributions to this volume represent this range of connections between K-theory, noncommmutative geometry, and other branches of mathematics. Algebraic geometry bicssc Proceedings, conferences, collections, etc. pertaining to \(K\)-theory msc Proceedings, conferences, collections, etc. pertaining to global analysis msc Noncommutative algebraic geometry msc (Co)homology theory in algebraic geometry msc Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.) msc Deformation quantization, star products msc Infinite-dimensional manifolds msc Cuntz edt Karoubi edt Nest edt Weibel edt https://ems.press/doi/10.4171/060 cover image https://content.ems.press/assets/public/images/books/cover-60.png nam a22 5a 4500 10.4171/057 DE-4084 2008-10-22 a fot 00| 0| cr nn mmmmamaa 081022e20081022gw fot 00| 0|eng d 9783037195574 10.4171/057 doi DE-4084 PBX bicssc PBW bicssc PHU bicssc PB bicssc 01-02 msc 82-02 msc 82C03 msc 82B40 msc Gallavotti edt Boltzmanns Legacy. EMS Press 2008 1 online resource (284 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda ESI Lectures in Mathematics and Physics (esi) 5 2943-4939 Restricted to subscribers. https://ems.press/books Ludwig Eduard Boltzmann (1844-1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. He was one of the most important advocates for atomic theory when that scientific model was still highly controversial. To commemorate the 100th anniversary of his death in Duino, the International Symposium Boltzmann's Legacy was held at the Erwin Schrödinger International Institute for Mathematical Physics in June 2006. This text covers a wide spectrum of topics ranging from equilibrium statistical and nonequilibrium statistical physics, ergodic theory and chaos to basic questions of biology and historical accounts of Boltzmann's work. Besides the lectures presented at the symposium the volume also contains contributions specially written for this occasion. The articles give a broad overview of Boltzmann's legacy to the sciences from the standpoint of some of present day's leading scholars in the field. The book addresses students and researchers in mathematics, physics and the history of science. History of mathematics bicssc Applied mathematics bicssc Mathematical physics bicssc Mathematics bicssc Research exposition (monographs, survey articles) pertaining to history and biography msc Research exposition (monographs, survey articles) pertaining to statistical mechanics msc Foundations of time-dependent statistical mechanics msc Kinetic theory of gases in equilibrium statistical mechanics msc Reiter edt Yngvason edt https://ems.press/doi/10.4171/057 cover image https://content.ems.press/assets/public/images/books/cover-61.png nam a22 5a 4500 10.4171/068 DE-4084 2009-01-10 a fot 00| 0| cr nn mmmmamaa 090110e20090110gw fot 00| 0|eng d 9783037195680 10.4171/068 doi DE-4084 PBKJ bicssc PBW bicssc PB bicssc 83C57 msc 35L70 msc 35Q75 msc 58J45 msc 83C75 msc Christodoulou aut The Formation of Black Holes in General Relativity. EMS Press 2009 1 online resource (599 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Monographs in Mathematics (emm) 4 2523-5206 Restricted to subscribers. https://ems.press/books In 1965 Penrose introduced the fundamental concept of a trapped surface, on the basis of which he proved a theorem which asserts that a spacetime containing such a surface must come to an end. The presence of a trapped surface implies, moreover, that there is a region of spacetime, the black hole, which is inaccessible to observation from infinity. A major challenge since that time has been to find out how trapped surfaces actually form, by analyzing the dynamics of gravitational collapse. The present monograph achieves this aim by establishing the formation of trapped surfaces in pure general relativity through the focusing of gravitational waves. The theorems proved in the present monograph constitute the first foray into the long-time dynamics of general relativity in the large, that is, when the initial data are no longer confined to a suitable neighborhood of trivial data. The main new method, the short pulse method, applies to general systems of Euler-Lagrange equations of hyperbolic type, and provides the means to tackle problems which have hitherto seemed unapproachable. This monograph will be of interest to people working in general relativity, geometric analysis, and partial differential equations. Differential calculus & equations bicssc Applied mathematics bicssc Mathematics bicssc Black holes msc Second-order nonlinear hyperbolic equations msc PDEs in connection with relativity and gravitational theory msc Hyperbolic equations on manifolds msc Space-time singularities, cosmic censorship, etc. msc https://ems.press/doi/10.4171/068 cover image https://content.ems.press/assets/public/images/books/cover-62.png nam a22 5a 4500 10.4171/059 DE-4084 2008-12-01 a fot 00| 0| cr nn mmmmamaa 081201e20081201gw fot 00| 0|eng d 9783037195598 10.4171/059 doi DE-4084 PBX bicssc 01-02 msc Beery edt Thomas Harriots Doctrine of Triangular Numbers: the Magisteria Magna. EMS Press 2008 1 online resource (144 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 2 2523-5222 Restricted to subscribers. https://ems.press/books Thomas Harriot (c.1560-1621) was a mathematician and astronomer, known not only for his work in algebra and geometry, but also for his wide-ranging interests in ballistics, navigation, and optics (he discovered the sine law of refraction now known as Snells law). By about 1614, Harriot had developed finite difference interpolation methods for navigational tables. In 1618 (or slightly later) he composed a treatise entitled De numeris triangularibus et inde de progressionibus arithmeticis, Magisteria magna, in which he derived symbolic interpolation formulae and showed how to use them. This treatise was never published and is here reproduced for the first time. Commentary has been added to help the reader to follow Harriots beautiful but almost completely nonverbal presentation. The introductory essay preceding the treatise gives an overview of the contents of the Magisteria and describes its influence on Harriots contemporaries and successors over the next sixty years. Harriots method was not superseded until Newton, apparently independently, made a similar discovery in the 1660s. The ideas in the Magisteria were spread primarily through personal communication and unpublished manuscripts, and so, quite apart from their intrinsic mathematical interest, their survival in England during the seventeenth century provides an important case study in the dissemination of mathematics through informal networks of friends and acquaintances. History of mathematics bicssc Research exposition (monographs, survey articles) pertaining to history and biography msc Stedall edt https://ems.press/doi/10.4171/059 cover image https://content.ems.press/assets/public/images/books/cover-64.jpg nam a22 5a 4500 10.4171/055 DE-4084 2009-03-25 a fot 00| 0| cr nn mmmmamaa 090325e20090325gw fot 00| 0|eng d 9783037195550 10.4171/055 doi DE-4084 PBKD bicssc 30-00 msc 32-00 msc 32G15 msc 30F60 msc 14A20 msc 14C17 msc 14D20 msc 14H15 msc 14H60 msc 14L24 msc 14L35 msc 16R30 msc 20F36 msc 20F38 msc 20F65 msc 22F10 msc 20H10 msc 30F10 msc 30F15 msc 30F20 msc 30F25 msc 30C62 msc 51N15 msc 53A20 msc 53A35 msc 53B35 msc 53C24 msc 53C25 msc 53C50 msc 57M07 msc 57M60 msc 57R20 msc Papadopoulos edt Handbook of Teichmüller Theory, Volume II. EMS Press 2009 1 online resource (883 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 13 2523-5141 Restricted to subscribers. https://ems.press/books This multi-volume set deals with Teichmüller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmüller theory. The aim is to give a complete panorama of this generalized Teichmüller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The present volume has 19 chapters and is divided into four parts: * The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmüller spaces, cohomology of moduli space, and the intersection theory of moduli space). * The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). * Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). * The Grothendieck-Teichmüller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmüller theory of the soleniod). This handbook is an essential reference for graduate students and researchers interested in Teichmüller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field. Complex analysis, complex variables bicssc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functions of a complex variable msc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to several complex variables and analytic spaces msc Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) msc Teichmüller theory for Riemann surfaces msc Generalizations (algebraic spaces, stacks) msc Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry msc Algebraic moduli problems, moduli of vector bundles msc Families, moduli of curves (analytic) msc Vector bundles on curves and their moduli msc Geometric invariant theory msc Classical groups (algebro-geometric aspects) msc Trace rings and invariant theory (associative rings and algebras) msc Braid groups; Artin groups msc Other groups related to topology or analysis msc Geometric group theory msc Measurable group actions msc Fuchsian groups and their generalizations (group-theoretic aspects) msc Compact Riemann surfaces and uniformization msc Harmonic functions on Riemann surfaces msc Classification theory of Riemann surfaces msc Ideal boundary theory for Riemann surfaces msc Quasiconformal mappings in the complex plane msc Projective analytic geometry msc Projective differential geometry msc Non-Euclidean differential geometry msc Local differential geometry of Hermitian and Kählerian structures msc Rigidity results msc Special Riemannian manifolds (Einstein, Sasakian, etc.) msc Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics msc Topological methods in group theory msc Group actions on manifolds and cell complexes in low dimensions msc Characteristic classes and numbers in differential topology msc https://ems.press/doi/10.4171/055 cover image https://content.ems.press/assets/public/images/books/cover-65.png nam a22 5a 4500 10.4171/066 DE-4084 2009-04-08 a fot 00| 0| cr nn mmmmamaa 090408e20090408gw fot 00| 0|eng d 9783037195666 10.4171/066 doi DE-4084 PBV bicssc 05-02 msc 51-02 msc 05B05 msc 05B25 msc 51B10 msc 51B15 msc 51B20 msc 51E05 msc 51E12 msc 51E14 msc 51E20 msc 51E21 msc 51E30 msc Payne aut Finite Generalized Quadrangles ; Second Edition. EMS Press 2009 1 online resource (299 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 9 2523-5184 Restricted to subscribers. https://ems.press/books Generalized quadrangles (GQ) were formally introduced by J. Tits in 1959 in order to describe geometric properties of simple groups of Lie type of rank 2. After its appearance in 1984, _Finite Generalized Quadrangles_ (FGQ) quickly became the standard reference for finite GQ. It presents the whole story of the subject from the very beginning in a book of modest length. This second edition is essentially a reprint of the first edition. It is a careful rendering into LaTeX of the original, along with an appendix that introduces major new results pertaining to GQ, especially in those areas in which the authors of this work have made a contribution. The first edition has been out of print for many years, and the new edition makes again available this classical reference in the rapidly increasing field of finite geometries. Combinatorics & graph theory bicssc Research exposition (monographs, survey articles) pertaining to combinatorics msc Research exposition (monographs, survey articles) pertaining to geometry msc Combinatorial aspects of block designs msc Combinatorial aspects of finite geometries msc Möbius geometries msc Laguerre geometries msc Minkowski geometries in nonlinear incidence geometry msc General block designs in finite geometry msc Generalized quadrangles and generalized polygons in finite geometry msc Finite partial geometries (general), nets, partial spreads msc Combinatorial structures in finite projective spaces msc Blocking sets, ovals, \(k\)-arcs msc Other finite incidence structures (geometric aspects) msc Thas aut https://ems.press/doi/10.4171/066 cover image https://content.ems.press/assets/public/images/books/cover-67.png nam a22 5a 4500 10.4171/056 DE-4084 2009-06-15 a fot 10| 0| cr nn mmmmamaa 090615e20090615gw fot 10| 0|eng d 9783037195567 10.4171/056 doi DE-4084 PBKJ bicssc 00Bxx msc Jeltsch edt 6th International Congress on Industrial and Applied Mathematics ; Zürich, Switzerland, 16-20 July 2007, Invited Lectures. EMS Press 2009 1 online resource (530 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books The International Council for Industrial and Applied Mathematics (ICIAM) is the worldwide organisation of societies which are dedicated primarily or significantly to applied and/or industrial mathematics. The ICIAM Congresses, held every 4 years, are run under the auspices of the Council with the aim to advance the applications of mathematics in all parts of the world. The 6th ICIAM Congress was held in Zürich, Switzerland, 16-20 July 2007, and was attended by more than 3000 scientists from 47 countries. This volume collects the invited lectures of this Congres, the appreciations of the ICIAM Prize winners achievements and the Euler Lecture celebrating the 300th anniversary of Euler. The authors of these papers are leading researchers of their fields, rigorously selected by a distinguished international program committee. The book presents an overview of contemporary applications of mathematics, new perspectives and open problems. Topics embrace analysis of and numerical methods for: * linear and nonlinear partial differential equations * multiscale modeling * nonlinear problems involving integral operators * controllability and observability * asymptotic solutions of Hamilton-Jacobi equations * contact problems in solid mechanics * topology optimization of structures * dissipation inequalities in systems theory * greedy algorithms * sampling in function space * order-value optimization * parabolic partial differential equations and deterministic games Moreover, particular applications involve risk in financial markets, radar imaging, brain dynamics, complex geometric optics applied to acoustics and electromagnetics. Differential calculus & equations bicssc Conference proceedings and collections of articles msc Wanner edt https://ems.press/doi/10.4171/056 cover image https://content.ems.press/assets/public/images/books/cover-63.png nam a22 5a 4500 10.4171/053 DE-4084 2009-06-08 a fot 00| 0| cr nn mmmmamaa 090608e20090608gw fot 00| 0|eng d 9783037195536 10.4171/053 doi DE-4084 PBW bicssc PHR bicssc PHU bicssc PBKJ bicssc 83-02 msc 83C75 msc Ringström aut The Cauchy Problem in General Relativity. EMS Press 2009 1 online resource (307 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda ESI Lectures in Mathematics and Physics (esi) 6 2943-4939 Restricted to subscribers. https://ems.press/books The general theory of relativity is a theory of manifolds equipped with Lorentz metrics and fields which describe the matter content. Einsteins equations equate the Einstein tensor (a curvature quantity associated with the Lorentz metric) with the stress energy tensor (an object constructed using the matter fields). In addition, there are equations describing the evolution of the matter. Using symmetry as a guiding principle, one is naturally led to the Schwarzschild and Friedmann-Lemaître-Robertson-Walker solutions, modelling an isolated system and the entire universe respectively. In a different approach, formulating Einsteins equations as an initial value problem allows a closer study of their solutions. This book first provides a definition of the concept of initial data and a proof of the correspondence between initial data and development. It turns out that some initial data allow non-isometric maximal developments, complicating the uniqueness issue. The second half of the book is concerned with this and related problems, such as strong cosmic censorship. The book presents complete proofs of several classical results that play a central role in mathematical relativity but are not easily accessible to those wishing to enter the subject. Prerequisites are a good knowledge of basic measure and integration theory as well as the fundamentals of Lorentz geometry. The necessary background from the theory of partial differential equations and Lorentz geometry is included. Applied mathematics bicssc Relativity physics bicssc Mathematical physics bicssc Differential calculus & equations bicssc Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory msc Space-time singularities, cosmic censorship, etc. msc https://ems.press/doi/10.4171/053 cover image https://content.ems.press/assets/public/images/books/cover-66.png nam a22 5a 4500 10.4171/070 DE-4084 2009-07-08 a fot 00| 0| cr nn mmmmamaa 090708e20090708gw fot 00| 0|eng d 9783037195703 10.4171/070 doi DE-4084 PBK bicssc PBT bicssc PHD bicssc PHDD bicssc PB bicssc 82-02 msc 82B10 msc 46G12 msc 46T12 msc 60G60 msc 60J25 msc Albeverio aut The Statistical Mechanics of Quantum Lattice Systems ; A Path Integral Approach. EMS Press 2009 1 online resource (392 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 8 2943-5005 Restricted to subscribers. https://ems.press/books Quantum statistical mechanics plays a major role in many fields such as, for instance, thermodynamics, plasma physics, solid-state physics, and the study of stellar structure. While the theory of quantum harmonic oscillators is relatively simple, the case of anharmonic oscillators, a mathematical model of a localized quantum particle, is more complex and challenging. Moreover, infinite systems of interacting quantum anharmonic oscillators possess interesting ordering properties with respect to quantum stabilization. This book presents a rigorous approach to the statistical mechanics of such systems, in particular with respect to their actions on a crystal lattice. The text is addressed to both mathematicians and physicists, especially those who are concerned with the rigorous mathematical background of their results and the kind of problems that arise in quantum statistical mechanics. The reader will find here a concise collection of facts, concepts, and tools relevant for the application of path integrals and other methods based on measure and integration theory to problems of quantum physics, in particular the latest results in the mathematical theory of quantum anharmonic crystals. The methods developed in the book are also applicable to other problems involving infinitely many variables, for example, in biology and economics. Calculus & mathematical analysis bicssc Probability & statistics bicssc Classical mechanics bicssc Analytical mechanics bicssc Mathematics bicssc Research exposition (monographs, survey articles) pertaining to statistical mechanics msc Quantum equilibrium statistical mechanics (general) msc Measures and integration on abstract linear spaces msc Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds msc Random fields msc Continuous-time Markov processes on general state spaces msc Kondratiev aut Kozitsky aut Röckner aut https://ems.press/doi/10.4171/070 cover image https://content.ems.press/assets/public/images/books/cover-68.png nam a22 5a 4500 10.4171/069 DE-4084 2009-06-24 a fot 00| 0| cr nn mmmmamaa 090624e20090624gw fot 00| 0|eng d 9783037195697 10.4171/069 doi DE-4084 PBK bicssc PB bicssc 65-XX msc 01-XX msc Novak aut Essays on the Complexity of Continuous Problems. EMS Press 2009 1 online resource (105 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books This book contains five essays on the complexity of continuous problems, written for a wider audience. * Henryk Woźniakowski and the complexity of continuous problems * Complexity as a new challenge for mathematicians * A brief history of information-based complexity * How high is high-dimensional? * What is information-based complexity? The first four essays are based on talks presented in 2008 when Henryk Woźniakowski received an honorary doctoral degree of the Friedrich Schiller University of Jena. The focus is on introduction and history of the complexity of continuous problems, as well as on recent progress concerning the complexity of high-dimensional numerical problems. The last essay provides a brief and informal introduction to the basic notions and concepts of information-based complexity addressed to a general readership. Calculus & mathematical analysis bicssc Mathematics bicssc Numerical analysis msc History and biography msc Sloan aut Traub aut Woźniakowski aut https://ems.press/doi/10.4171/069 cover image https://content.ems.press/assets/public/images/books/cover-69.png nam a22 5a 4500 10.4171/064 DE-4084 2009-08-08 a fot 00| 0| cr nn mmmmamaa 090808e20090808gw fot 00| 0|eng d 9783037195642 10.4171/064 doi DE-4084 PBMW bicssc 14-01 msc 14E05 msc 14E07 msc 14H50 msc 14J26 msc 14J70 msc 14M99 msc 14N05 msc Beltrametti aut Lectures on Curves, Surfaces and Projective Varieties ; A Classical View of Algebraic Geometry. EMS Press 2009 1 online resource (506 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 8 2943-4955 Restricted to subscribers. https://ems.press/books This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students of the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses on the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature. First corrected reprint, June 2012. Algebraic geometry bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry msc Rational and birational maps msc Birational automorphisms, Cremona group and generalizations msc Plane and space curves msc Rational and ruled surfaces msc Hypersurfaces and algebraic geometry msc Special varieties msc Projective techniques in algebraic geometry msc Carletti aut Gallarati aut Monti Bragadin aut https://ems.press/doi/10.4171/064 cover image https://content.ems.press/assets/public/images/books/cover-70.png nam a22 5a 4500 10.4171/071 DE-4084 2009-08-15 a fot 00| 0| cr nn mmmmamaa 090815e20090815gw fot 00| 0|eng d 9783037195710 10.4171/071 doi DE-4084 PBT bicssc 60-01 msc 60J10 msc 60J50 msc 60J80 msc 60G50 msc 05C05 msc 94C05 msc Woess aut Denumerable Markov Chains ; Generating Functions, Boundary Theory, Random Walks on Trees. EMS Press 2009 1 online resource (368 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 9 2943-4955 Restricted to subscribers. https://ems.press/books Markov chains are the first and most important examples of random processes. This book is about time-homogeneous Markov chains that evolve with discrete time steps on a countable state space. Measure theory is not avoided, careful and complete proofs are provided. A specific feature is the systematic use, on a relatively elementary level, of generating functions associated with transition probabilities for analyzing Markov chains. Basic definitions and facts include the construction of the trajectory space and are followed by ample material concerning recurrence and transience, the convergence and ergodic theorems for positive recurrent chains. There is a side-trip to the Perron-Frobenius theorem. Special attention is given to reversible Markov chains and to basic mathematical models of population evolution such as birth-and-death chains, Galton-Watson process and branching Markov chains. A good part of the second half is devoted to the introduction of the basic language and elements of the potential theory of transient Markov chains. Here the construction and properties of the Martin boundary for describing positive harmonic functions are crucial. In the long final chapter on nearest neighbour random walks on (typically infinite) trees the reader can harvest from the seed of methods laid out so far, in order to obtain a rather detailed understanding of a specific, broad class of Markov chains. The level varies from basic to more advanced, addressing an audience from masters degree students to researchers in mathematics, and persons who want to teach the subject on a medium or advanced level. A specific characteristic of the book is the rich source of classroom-tested exercises with solutions. Probability & statistics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory msc Markov chains (discrete-time Markov processes on discrete state spaces) msc Boundary theory for Markov processes msc Branching processes (Galton-Watson, birth-and-death, etc.) msc Sums of independent random variables; random walks msc Trees msc Analytic circuit theory msc https://ems.press/doi/10.4171/071 cover image https://content.ems.press/assets/public/images/books/cover-80.jpg nam a22 5a 4500 10.4171/046 DE-4084 2009-08-29 a fot 00| 0| cr nn mmmmamaa 090829e20090829gw fot 00| 0|eng d 9783037195468 10.4171/046 doi DE-4084 PBWL bicssc 37-02 msc 60-02 msc Weber aut Dynamical Systems and Processes. EMS Press 2009 1 online resource (773 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 14 2523-5141 Restricted to subscribers. https://ems.press/books This book presents in a concise and accessible way, as well as in a common setting, various tools and methods arising from spectral theory, ergodic theory and stochastic processes theory, which form the basis of and contribute interactively a great deal to the current research on almost everywhere convergence problems. The text is divided into four parts. Part I is devoted to spectral results such as von Neumanns theorem, spectral regularizations inequalities and their link with square functions and entropy numbers of ergodic averages. The representation of a weakly stationary process as Fourier transform of some random orthogonal measure, and a study of Gaposhkins spectral criterion conclude this part. Classical results such as mixing in dynamical systems, Birkhoffs pointwise theorem, dominated ergodic theorems, oscillations functions of ergodic averages, transference principle, Wiener-Wintner theorem, Banach principle, continuity principle, Bourgains entropy criteria, Burton-Denkers central limit theorem are covered in part II. The metric entropy method and the majorizing measure method, including a succinct study of Gaussian processes, are treated in part III, with applications to suprema of random polynomials. Part IV contains a study of Riemann sums and of the convergence properties of the system \{ f(n_k x), k \geq 1 \}, as well as a probabilistic approach concerning divisors with applications. Researchers working in dynamical systems and at the crossroads of spectral theory, ergodic theory and stochastic processes will find the tools, methods and results presented in this book of great interest. It is written in a style accessible to graduate students throughout. Stochastics bicssc Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory msc Research exposition (monographs, survey articles) pertaining to probability theory msc https://ems.press/doi/10.4171/046 cover image https://content.ems.press/assets/public/images/books/cover-72.png nam a22 5a 4500 10.4171/073 DE-4084 2009-09-24 a fot 00| 0| cr nn mmmmamaa 090924e20090924gw fot 00| 0|eng d 9783037195734 10.4171/073 doi DE-4084 PBMW bicssc PBKJ bicssc PBMW bicssc 14F42 msc 34M30 msc 34M35 msc 34M40 msc 81T15 msc 81T18 msc 81T75 msc 11S40 msc 33B30 msc 34M50 msc Connes edt Renormalization and Galois Theories. EMS Press 2009 1 online resource (279 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 15 2523-5141 Restricted to subscribers. https://ems.press/books This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory. The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions. The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes, orchestrated by diverse Galois theories. It contains three lecture courses together with five research articles and will be useful to both reseachers and graduate students in mathematics and physics. Algebraic geometry bicssc Differential calculus & equations bicssc Algebraic geometry bicssc Motivic cohomology; motivic homotopy theory msc Asymptotics and summation methods for ordinary differential equations in the complex domain msc Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms msc Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain msc Perturbative methods of renormalization applied to problems in quantum field theory msc Feynman diagrams msc Noncommutative geometry methods in quantum field theory msc Zeta functions and \(L\)-functions msc Higher logarithm functions msc Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain msc Fauvet edt Ramis edt https://ems.press/doi/10.4171/073 cover image https://content.ems.press/assets/public/images/books/cover-71.png nam a22 5a 4500 10.4171/074 DE-4084 2009-10-01 a fot 00| 0| cr nn mmmmamaa 091001e20091001gw fot 00| 0|eng d 9783037195741 10.4171/074 doi DE-4084 PBMW bicssc PBH bicssc PB bicssc 11-02 msc 14-02 msc Böckle aut Cohomological Theory of Crystals over Function Fields. EMS Press 2009 1 online resource (195 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 9 2943-5005 Restricted to subscribers. https://ems.press/books This book develops a new cohomological theory for schemes in positive characteristic p and it applies this theory to give a purely algebraic proof of a conjecture of Goss on the rationality of certain L\-functions arising in the arithmetic of function fields. These L\-functions are power series over a certain ring A, associated to any family of Drinfeld A\-modules or, more generally, of A\-motives on a variety of finite type over the finite field **F**p. By analogy to the Weil conjecture, Goss conjectured that these L\-functions are in fact rational functions. In 1996 Taguchi and Wan gave a first proof of Gosss conjecture by analytic methods à la Dwork. The present text introduces A\-crystals, which can be viewed as generalizations of families of A\-motives, and studies their cohomology. While A\-crystals are defined in terms of coherent sheaves together with a Frobenius map, in many ways they actually behave like constructible étale sheaves. A central result is a Lefschetz trace formula for L\-functions of A\-crystals, from which the rationality of these L\-functions is immediate. Beyond its application to Gosss L\-functions, the theory of A\-crystals is closely related to the work of Emerton and Kisin on unit root F\-crystals, and it is essential in an Eichler-Shimura type isomorphism for Drinfeld modular forms as constructed by the first author. The book is intended for researchers and advanced graduate students interested in the arithmetic of function fields and/or cohomology theories for varieties in positive characteristic. It assumes a good working knowledge in algebraic geometry as well as familiarity with homological algebra and derived categories, as provided by standard textbooks. Beyond that the presentation is largely self-contained. Algebraic geometry bicssc Number theory bicssc Mathematics bicssc Research exposition (monographs, survey articles) pertaining to number theory msc Research exposition (monographs, survey articles) pertaining to algebraic geometry msc Pink aut https://ems.press/doi/10.4171/074 cover image https://content.ems.press/assets/public/images/books/cover-74.png nam a22 5a 4500 10.4171/058 DE-4084 2009-10-30 a fot 00| 0| cr nn mmmmamaa 091030e20091030gw fot 00| 0|eng d 9783037195581 10.4171/058 doi DE-4084 PBX bicssc 00B60 msc 01A75 msc Springer edt Hans Freudenthal, Selecta. EMS Press 2009 1 online resource (661 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 3 2523-5222 Restricted to subscribers. https://ems.press/books Hans Freudenthal (1905-1990) was a Dutch mathematician, born in Luckenwalde, Germany. His scientific activities were of a rich variety. Enrolling at the University of Berlin as a student in the 1920s, he followed in the footsteps of his teachers, and became a topologist, but with a lively interest in group theory. Later in life, after a long journey through the realm of mathematics, working on almost all subjects that drew his interest, he turned towards the practical and methodological issues of the didactics of mathematics. The present Selecta are devoted to Freudenthals mathematical oeuvre, they contain a selection of his major contributions. Included are fundamental contributions to topology such as the foundation of the theory of ends (in the thesis of 1931), the introduction (in 1937) of the suspension and its use in stability results for homotopy groups of spheres. In group theory there is work on topological groups (of the 1930s) and on various aspects of the theory of Lie groups, such as a paper on automorphisms of 1941. From the later work of the 1950s and 1960s, papers on geometric aspects of Lie theory (geometries associated to exceptional groups, space problems) have been included. Freudenthals versatility is further demonstrated by a choice from his foundational and historical work: papers on intuitionistic logic and topology, a paper on axiomatic geometry reappraising Hilberts _Grundlagen_, and a paper summarizing his development of Lincos, a universal (cosmic) language. The book also contains a sketch of Freudenthals life. Most of the selected papers are accompanied by brief comments. History of mathematics bicssc Collections of reprinted articles msc Collected or selected works; reprintings or translations of classics msc van Dalen edt https://ems.press/doi/10.4171/058 cover image https://content.ems.press/assets/public/images/books/cover-73.jpg nam a22 5a 4500 10.4171/128 DE-4084 2013-12-13 a fot 00| 0| cr nn mmmmamaa 131213e20131213gw fot 00| 0|eng d 9783037196281 10.4171/128 doi DE-4084 PBKA bicssc PBK bicssc 58-02 msc 58B34 msc Khalkhali aut Basic Noncommutative Geometry ; Second edition. EMS Press 2013 1 online resource (257 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 10 2523-5184 Restricted to subscribers. https://ems.press/books This text provides an introduction to noncommutative geometry and some of its applications. It can be used either as a textbook for a graduate course or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well. Two new sections have been added to this second edition: one concerns the Gauss-Bonnet theorem and the definition and computation of the scalar curvature of the curved noncommutative two torus, and the second is a brief introduction to Hopf cyclic cohomology. The bibliography has been extended and some new examples are presented. For the first edition of this book, please click [here](https://doi.org/10.4171/061). Calculus bicssc Calculus & mathematical analysis bicssc Research exposition (monographs, survey articles) pertaining to global analysis msc Noncommutative geometry (à la Connes) msc https://ems.press/doi/10.4171/128 cover image https://content.ems.press/assets/public/images/books/cover-225.png nam a22 5a 4500 10.4171/076 DE-4084 2010-02-26 a fot 00| 0| cr nn mmmmamaa 100226e20100226gw fot 00| 0|eng d 9783037195765 10.4171/076 doi DE-4084 PBKJ bicssc 32-02 msc 32W05 msc 35N15 msc Straube aut Lectures on the -Sobolev Theory of the -Neumann problem. EMS Press 2010 1 online resource (214 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda ESI Lectures in Mathematics and Physics (esi) 7 2943-4939 Restricted to subscribers. https://ems.press/books This book provides a thorough and self-contained introduction to the \overline{\partial}-Neumann problem, leading up to current research, in the context of the \mathcal{L}^2-Sobolev theory on bounded pseudoconvex domains in \mathbb{C}^n. It grew out of courses for advanced graduate students and young researchers given by the author at the Erwin Schrödinger International Institute for Mathematical Physics and at Texas A&M University. The introductory chapter provides an overview of the contents and puts them in historical perspective. The second chapter presents the basic \mathcal{L}^2-theory. Following is a chapter on the subelliptic estimates on strictly pseudoconvex domains. The two final chapters on compactness and on regularity in Sobolev spaces bring the reader to the frontiers of research. Prerequisites are a solid background in basic complex and functional analysis, including the elementary \mathcal{L}^2-Sobolev theory and distributions. Some knowledge in several complex variables is helpful. Concerning partial differential equations, not much is assumed. The elliptic regularity of the Dirichlet problem for the Laplacian is quoted a few times, but the ellipticity results needed for elliptic regularization in the third chapter are proved from scratch. Differential calculus & equations bicssc Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces msc \(\overline\partial\) and \(\overline\partial\)-Neumann operators msc \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs msc https://ems.press/doi/10.4171/076 cover image https://content.ems.press/assets/public/images/books/cover-78.png nam a22 5a 4500 10.4171/077 DE-4084 2010-04-24 a fot 10| 0| cr nn mmmmamaa 100424e20100424gw fot 10| 0|eng d 9783037195772 10.4171/077 doi DE-4084 PB bicssc 00Bxx msc Ran edt European Congress of Mathematics ; Amsterdam, 14-18 July, 2008. EMS Press 2010 1 online resource (488 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books The European Congress of Mathematics, held every four years, has established itself as a major international mathematical event. Following those in Paris (1992), Budapest (1996), Barcelona (2000) and Stockholm (2004), the Fifth European Congress of Mathematics (5ECM) took place in Amsterdam, The Netherlands, July 14-18, 2008, with about 1000 participants from 68 different countries. Ten plenary and thirty-three invited lectures were delivered. Three science lectures outlined applications of mathematics in other sciences: climate change, quantum information theory and population dynamics. As in the four preceding EMS congresses, ten EMS prizes were granted to very promising young mathematicians. In addition, the Felix Klein Prize was awarded, for the second time, for an application of mathematics to a concrete and difficult industrial problem. There were twenty-two minisymposia, spread over the whole mathematical area. Two round table meetings were organized: one on industrial mathematics and one on mathematics and developing countries. As part of the 44th Nederlands Mathematisch Congres, which was embedded in 5ECM, the so-called Brouwer lecture was presented. It is the Netherland's most prestigious award in mathematics, organized every three years by the Royal Dutch Mathematical Society. Information about Brouwer was given in an invited historical lecture during the congress. These proceedings contain a selection of the contributions to the congress, providing a permanent record of the best what mathematics offers today. Mathematics bicssc Conference proceedings and collections of articles msc te Riele edt Wiegerinck edt https://ems.press/doi/10.4171/077 cover image https://content.ems.press/assets/public/images/books/cover-75.png nam a22 5a 4500 10.4171/078 DE-4084 2010-04-30 a fot 00| 0| cr nn mmmmamaa 100430e20100430gw fot 00| 0|eng d 9783037195789 10.4171/078 doi DE-4084 PBKJ bicssc 35L65 msc 35K65 msc 65M99 msc 65M15 msc 65M12 msc 35L67 msc 35D30 msc 47N40 msc 35A35 msc Holden aut Splitting Methods for Partial Differential Equations with Rough Solutions ; Analysis and MATLAB programs. EMS Press 2010 1 online resource (234 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 11 2523-5184 Restricted to subscribers. https://ems.press/books Operator splitting (or the fractional steps method) is a very common tool to analyze nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated model one can often split it into simpler problems that can be analyzed separately. In this book one studies operator splitting for a family of nonlinear evolution equations, including hyperbolic conservation laws and degenerate convection-diffusion equations. Common for these equations is the prevalence of rough, or non-smooth, solutions, e.g., shocks. Rigorous analysis is presented, showing that both semi-discrete and fully discrete splitting methods converge. For conservation laws, sharp error estimates are provided and for convection-diffusion equations one discusses a priori and a posteriori correction of entropy errors introduced by the splitting. Numerical methods include finite difference and finite volume methods as well as front tracking. The theory is illustrated by numerous examples. There is a dedicated web page that provides MATLAB codes for many of the examples. The book is suitable for graduate students and researchers in pure and applied mathematics, physics, and engineering. Differential calculus & equations bicssc Hyperbolic conservation laws msc Degenerate parabolic equations msc Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems msc Error bounds for initial value and initial-boundary value problems involving PDEs msc Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs msc Shocks and singularities for hyperbolic equations msc Weak solutions to PDEs msc Applications of operator theory in numerical analysis msc Theoretical approximation in context of PDEs msc Karlsen aut Lie aut Risebro aut https://ems.press/doi/10.4171/078 cover image https://content.ems.press/assets/public/images/books/cover-77.png nam a22 5a 4500 10.4171/081 DE-4084 2010-05-19 a fot 00| 0| cr nn mmmmamaa 100519e20100519gw fot 00| 0|eng d 9783037195819 10.4171/081 doi DE-4084 PBKJ bicssc PBKF bicssc PBKQ bicssc 37-01 msc 37A25 msc 37B25 msc 37C10 msc 37C20 msc 37C27 msc 37C29 msc 37C50 msc 37D05 msc 37J35 msc 37N05 msc 34C25 msc 34C28 msc 34C37 msc 34C45 msc 34D20 msc 70H15 msc 70H05 msc 70H25 msc 53D35 msc 53C24 msc 53D05 msc 58E05 msc 58E30 msc Zehnder aut Lectures on Dynamical Systems ; Hamiltonian Vector Fields and Symplectic Capacities. EMS Press 2010 1 online resource (363 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 10 2943-4955 Restricted to subscribers. https://ems.press/books This book originated from an introductory lecture course on dynamical systems given by the author for advanced students in mathematics and physics at the ETH Zurich. The first part centres around unstable and chaotic phenomena caused by the occurrence of homoclinic points. The existence of homoclinic points complicates the orbit structure considerably and gives rise to invariant hyperbolic sets nearby. The orbit structure in such sets is analyzed by means of the shadowing lemma, whose proof is based on the contraction principle. This lemma is also used to prove S. Smales theorem about the embedding of Bernoulli systems near homoclinic orbits. The chaotic behavior is illustrated in the simple mechanical model of a periodically perturbed mathematical pendulum. The second part of the book is devoted to Hamiltonian systems. The Hamiltonian formalism is developed in the elegant language of the exterior calculus. The theorem of V. Arnold and R. Jost shows that the solutions of Hamiltonian systems which possess sufficiently many integrals of motion can be written down explicitly and for all times. The existence proofs of global periodic orbits of Hamiltonian systems on symplectic manifolds are based on a variational principle for the old action functional of classical mechanics. The necessary tools from variational calculus are developed. There is an intimate relation between the periodic orbits of Hamiltonian systems and a class of symplectic invariants called symplectic capacities. From these symplectic invariants one derives surprising symplectic rigidity phenomena. This allows a first glimpse of the fast developing new field of symplectic topology. Differential calculus & equations bicssc Functional analysis & transforms bicssc Calculus of variations bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory msc Ergodicity, mixing, rates of mixing msc Stability of topological dynamical systems msc Dynamics induced by flows and semiflows msc Generic properties, structural stability of dynamical systems msc Periodic orbits of vector fields and flows msc Homoclinic and heteroclinic orbits for dynamical systems msc Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics msc Dynamical systems with hyperbolic orbits and sets msc Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests msc Dynamical systems in classical and celestial mechanics msc Periodic solutions to ordinary differential equations msc Complex behavior and chaotic systems of ordinary differential equations msc Homoclinic and heteroclinic solutions to ordinary differential equations msc Invariant manifolds for ordinary differential equations msc Stability of solutions to ordinary differential equations msc Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics msc Hamilton's equations msc Hamilton's principle msc Global theory of symplectic and contact manifolds msc Rigidity results msc Symplectic manifolds (general theory) msc Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces msc Variational principles in infinite-dimensional spaces msc https://ems.press/doi/10.4171/081 cover image https://content.ems.press/assets/public/images/books/cover-76.png nam a22 5a 4500 10.4171/086 DE-4084 2010-06-01 a fot 00| 0| cr nn mmmmamaa 100601e20100601gw fot 00| 0|eng d 9783037195864 10.4171/086 doi DE-4084 PBP bicssc PBF bicssc PBPD bicssc 57-02 msc 81-02 msc 16-02 msc 18-02 msc Turaev aut Homotopy Quantum Field Theory ; With Appendices by Michael Müger and Alexis Virelizier. EMS Press 2010 1 online resource (290 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 10 2943-5005 Restricted to subscribers. https://ems.press/books Homotopy Quantum Field Theory (HQFT) is a branch of Topological Quantum Field Theory founded by E. Witten and M. Atiyah. It applies ideas from theoretical physics to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a fixed target space. This book is the first systematic exposition of Homotopy Quantum Field Theory. It starts with a formal definition of an HQFT and provides examples of HQFTs in all dimensions. The main body of the text is focused on 2-dimensional and 3-dimensional HQFTs. A study of these HQFTs leads to new algebraic objects: crossed Frobenius group-algebras, crossed ribbon group-categories, and Hopf group-coalgebras. These notions and their connections with HQFTs are discussed in detail. The text ends with several appendices including an outline of recent developments and a list of open problems. Three appendices by M. Müger and A. Virelizier summarize their work in this area. The book is addressed to mathematicians, theoretical physicists, and graduate students interested in topological aspects of quantum field theory. The exposition is self-contained and well suited for a one-semester graduate course. Prerequisites include only basics of algebra and topology. Topology bicssc Algebra bicssc Algebraic topology bicssc Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes msc Research exposition (monographs, survey articles) pertaining to quantum theory msc Research exposition (monographs, survey articles) pertaining to associative rings and algebras msc Research exposition (monographs, survey articles) pertaining to category theory msc https://ems.press/doi/10.4171/086 cover image https://content.ems.press/assets/public/images/books/cover-79.png nam a22 5a 4500 10.4171/085 DE-4084 2010-06-01 a fot 00| 0| cr nn mmmmamaa 100601e20100601gw fot 00| 0|eng d 9783037195857 10.4171/085 doi DE-4084 PBKF bicssc PB bicssc 46-02 msc 46E35 msc 42C40 msc 42B35 msc 68Q17 msc 41A55 msc Triebel aut Bases in Function Spaces, Sampling, Discrepancy, Numerical integration. EMS Press 2010 1 online resource (305 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 11 2943-5005 Restricted to subscribers. https://ems.press/books The first chapters of this book deal with Haar bases, Faber bases and some spline bases for function spaces in Euclidean n\-space and n\-cubes. This is used in the subsequent chapters to study sampling and numerical integration preferably in spaces with dominating mixed smoothness. The subject of the last chapter is the symbiotic relationship between numerical integration and discrepancy, measuring the deviation of sets of points from uniformity. This book is addressed to graduate students and mathematicians having a working knowledge of basic elements of function spaces and approximation theory, and who are interested in the subtle interplay between function spaces, complexity theory and number theory (discrepancy). Functional analysis & transforms bicssc Mathematics bicssc Research exposition (monographs, survey articles) pertaining to functional analysis msc Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems msc Nontrigonometric harmonic analysis involving wavelets and other special systems msc Function spaces arising in harmonic analysis msc Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) msc Approximate quadratures msc https://ems.press/doi/10.4171/085 cover image https://content.ems.press/assets/public/images/books/cover-82.png nam a22 5a 4500 10.4171/079 DE-4084 2010-06-10 a fot 00| 0| cr nn mmmmamaa 100610e20100610gw fot 00| 0|eng d 9783037195796 10.4171/079 doi DE-4084 PBMP bicssc 53-00 msc 53C26 msc 53C50 msc 81T60 msc 83E30 msc 83E50 msc 53C25 msc 53C29 msc 53C35 msc 53C10 msc Cortés edt Handbook of Pseudo-Riemannian Geometry and Supersymmetry. EMS Press 2010 1 online resource (964 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 16 2523-5141 Restricted to subscribers. https://ems.press/books The purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are: * special geometry and supersymmetry * generalized geometry * geometries with torsion * para-geometries * holonomy theory * symmetric spaces and spaces of constant curvature * conformal geometry * wave equations on Lorentzian manifolds * D-branes and K-theory The intended audience consists of advanced students and researchers working in differential geometry, string theory and related areas. The emphasis is on geometrical structures occurring on target spaces of supersymmetric field theories. Some of these structures can be fully described in the classical framework of pseudo-Riemannian geometry. Others lead to new concepts relating various fields of research, such as special Kähler geometry or generalized geometry. Differential & Riemannian geometry bicssc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to differential geometry msc Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry msc Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics msc Supersymmetric field theories in quantum mechanics msc String and superstring theories in gravitational theory msc Supergravity msc Special Riemannian manifolds (Einstein, Sasakian, etc.) msc Issues of holonomy in differential geometry msc Differential geometry of symmetric spaces msc \(G\)-structures msc https://ems.press/doi/10.4171/079 cover image https://content.ems.press/assets/public/images/books/cover-81.png nam a22 5a 4500 10.4171/084 DE-4084 2010-07-03 a fot 00| 0| cr nn mmmmamaa 100703e20100703gw fot 00| 0|eng d 9783037195840 10.4171/084 doi DE-4084 PBKS bicssc PB bicssc 65Y20 msc 68Q17 msc 68Q25 msc 41A63 msc 65-02 msc 46E22 msc 28C20 msc 46E30 msc 11K38 msc 65D32 msc Novak aut Tractability of Multivariate Problems. Volume II. Standard Information for Functionals EMS Press 2010 1 online resource (675 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 12 2943-5005 Restricted to subscribers. https://ems.press/books This three-volume set is a comprehensive study of the tractability of multivariate problems. The present second volume deals with algorithms using standard information consisting of function values for the approximation of linear and selected nonlinear functionals. An important example is numerical multivariate integration. The proof techniques used in volumes I and II are quite different. It is especially hard to establish meaningful lower error bounds for the approximation of functionals by using finitely many function values. Here, the concept of decomposable reproducing kernels is helpful, allowing it to find matching lower and upper error bounds for some linear functionals. It is then possible to conclude tractability results from such error bounds. Tractability results even for linear functionals are very rich in variety. There are infinite-dimensional Hilbert spaces for which the approximation with an arbitrarily small error of all linear functionals requires only one function value. There are Hilbert spaces for which all nontrivial linear functionals suffer from the curse of dimensionality. This holds for unweighted spaces, where the role of all variables and groups of variables is the same. For weighted spaces one can monitor the role of all variables and groups of variables. Necessary and sufficient conditions on the decay of the weights are given to obtain various notions of tractability. The text contains extensive chapters on discrepancy and integration, decomposable kernels and lower bounds, the Smolyak/sparse grid algorithms, lattice rules and the CBC (component-by-component) algorithms. This is done in various settings. Path integration and quantum computation are also discussed. The book is of interest for researchers working in computational mathematics, especially in approximation of high-dimensional problems. It is also well suited for graduate courses and seminars. 61 open problems are listed to stimulate future research in tractability. Numerical analysis bicssc Mathematics bicssc Complexity and performance of numerical algorithms msc Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) msc Analysis of algorithms and problem complexity msc Multidimensional problems msc Research exposition (monographs, survey articles) pertaining to numerical analysis msc Hilbert spaces with reproducing kernels ( (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) msc Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) msc Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) msc Irregularities of distribution, discrepancy msc Numerical quadrature and cubature formulas msc Woźniakowski aut https://ems.press/doi/10.4171/084 cover image https://content.ems.press/assets/public/images/books/cover-83.png nam a22 5a 4500 10.4171/093 DE-4084 2010-09-07 a fot 00| 0| cr nn mmmmamaa 100907e20100907gw fot 00| 0|eng d 9783037195932 10.4171/093 doi DE-4084 PBUH bicssc 05Axx msc 05Cxx msc 05Dxx msc 05Exx msc 11Dxx msc 11Hxx msc 11Pxx msc 13Pxx msc 14Qxx msc 15Axx msc 15Bxx msc 51Mxx msc 52Axx msc 52Bxx msc 52Cxx msc 62Hxx msc 62Kxx msc 62Qxx msc 65Cxx msc 68Qxx msc 68Rxx msc 68Wxx msc 90Bxx msc 90Cxx msc Onn aut Nonlinear Discrete Optimization ; An Algorithmic Theory. EMS Press 2010 1 online resource (147 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 13 2943-4971 Restricted to subscribers. https://ems.press/books This monograph develops an algorithmic theory of nonlinear discrete optimization. It introduces a simple and useful setup which enables the polynomial time solution of broad fundamental classes of nonlinear combinatorial optimization and integer programming problems in variable dimension. An important part of this theory is enhanced by recent developments in the algebra of Graver bases. The power of the theory is demonstrated by deriving the first polynomial time algorithms in a variety of application areas within operations research and statistics, including vector partitioning, matroid optimization, experimental design, multicommodity flows, multi-index transportation and privacy in statistical databases. The monograph is intended for graduate students and researchers. It is accessible to anyone with standard undergraduate knowledge and mathematical maturity. Linear programming bicssc Enumerative combinatorics msc Graph theory msc Extremal combinatorics msc Algebraic combinatorics msc Diophantine equations msc Geometry of numbers msc Additive number theory; partitions msc Computational aspects and applications of commutative rings msc Computational aspects in algebraic geometry msc Basic linear algebra msc Special matrices msc Real and complex geometry msc General convexity msc Polytopes and polyhedra msc Discrete geometry msc Multivariate analysis msc Design of statistical experiments msc Statistical tables msc Probabilistic methods, stochastic differential equations msc Theory of computing msc Discrete mathematics in relation to computer science msc Algorithms in computer science msc Operations research and management science msc Mathematical programming msc https://ems.press/doi/10.4171/093 cover image https://content.ems.press/assets/public/images/books/cover-84.jpg nam a22 5a 4500 10.4171/089 DE-4084 2010-08-24 a fot 00| 0| cr nn mmmmamaa 100824e20100824gw fot 00| 0|eng d 9783037195895 10.4171/089 doi DE-4084 PBX bicssc 00Bxx msc Colbois edt math.ch/100 ; Schweizerische Mathematische Gesellschaft - Société Mathématique Suisse - Swiss Mathematical Society 1910. EMS Press 2010 1 online resource (526 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books This book includes twenty-three essays to celebrate the 100th anniversary of the Swiss Mathematical Society. The life and work of outstanding mathematicians, extraordinary conferences held in Switzerland such as the three International Congresses of Mathematicians, the influence of women in Swiss mathematics are among the topics. The articles, including many photographs, old and recent, give a vivid picture of hundred years of mathematical life in Switzerland. Dieses Buch ist eine Festschrift zum 100-jährigen Bestehen der Schweizerischen Mathematischen Gesellschaft. Es enthält dreiundzwanzig Beiträge zur Mathematik in der Schweiz. Geschichtliches und Biographisches über herausragende Mathematiker an Schweizer Universitäten, grosse Tagungen wie etwa die drei Internationalen Mathematiker-Kongresse, die Rolle der Frauen in der Schweizer Mathematik sind nur einige Themen. Insgesamt vermitteln die verschiedenen Essays zusammen mit den zahlreichen Abbildungen ein höchst lebendiges und anschauliches Panorama eines Jahrhunderts Schweizer Mathematik. Cet ouvrage a été édité pour marquer le 100e anniversaire de la Société Mathématique Suisse. Il rassemble vingt-trois articles consacrés aux mathématiques en Suisse. Parmi beaucoup d'autres choses, les écrits évoquent la vie et l'uvre de grands mathématiciens des universités suisses, les grands événements, dont les trois Congrès internationaux de mathématiques, ou encore la présence des femmes dans les mathématiques suisses. Agrémenté de nombreuses photos, anciennes et récentes, ce livre donne une image très vivante de cent années de vie mathématique en Suisse. History of mathematics bicssc Conference proceedings and collections of articles msc Riedtmann edt Schroeder edt https://ems.press/doi/10.4171/089 cover image https://content.ems.press/assets/public/images/books/cover-85.png nam a22 5a 4500 10.4171/090 DE-4084 2010-09-29 a fot 00| 0| cr nn mmmmamaa 100929e20100929gw fot 00| 0|eng d 9783037195901 10.4171/090 doi DE-4084 PBH bicssc PB bicssc 20B05 msc 11F03 msc Harada aut Moonshine of Finite Groups. EMS Press 2010 1 online resource (83 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 12 2523-5184 Restricted to subscribers. https://ems.press/books This is an almost verbatim reproduction of the authors lecture notes written in 1983-84 at the Ohio State University, Columbus, Ohio, USA. A substantial update is given in the bibliography. Over the last 20 plus years, there has been an energetic activity in the field of finite simple group theory related to the monster simple group. Most notably, influential works have been produced in the theory of vertex operator algebras whose research was stimulated by the moonshine of the finite groups. Still, we can ask the same questions now just as we did some 30-40 years ago: What is the monster simple group? Is it really related to the theory of the universe as it was vaguely so envisioned? What lays behind the moonshine phenomena of the monster group? It may appear that we have only scratched the surface. These notes are primarily reproduced for the benefit of young readers who wish to start learning about modular functions used in moonshine. Number theory bicssc Mathematics bicssc General theory for finite permutation groups msc Modular and automorphic functions msc https://ems.press/doi/10.4171/090 cover image https://content.ems.press/assets/public/images/books/cover-86.png nam a22 5a 4500 10.4171/082 DE-4084 2010-09-29 a fot 00| 0| cr nn mmmmamaa 100929e20100929gw fot 00| 0|eng d 9783037195826 10.4171/082 doi DE-4084 PBP bicssc PBMP bicssc PBMP bicssc 57-02 msc 57M50 msc Bessières aut Geometrisation of 3-Manifolds. EMS Press 2010 1 online resource (247 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 13 2943-5005 Restricted to subscribers. https://ems.press/books The Geometrisation Conjecture was proposed by William Thurston in the mid 1970s in order to classify compact 3-manifolds by means of a canonical decomposition along essential, embedded surfaces into pieces that possess geometric structures. It contains the famous Poincaré Conjecture as a special case. In 2002, Grigory Perelman announced a proof of the Geometrisation Conjecture based on Richard Hamiltons Ricci flow approach, and presented it in a series of three celebrated arXiv preprints. Since then there has been an ongoing effort to understand Perelmans work by giving more detailed and accessible presentations of his ideas or alternative arguments for various parts of the proof. This book is a contribution to this endeavour. Its two main innovations are first a simplified version of Perelmans Ricci flow with surgery, which is called Ricci flow with bubbling-off, and secondly a completely different and original approach to the last step of the proof. In addition, special effort has been made to simplify and streamline the overall structure of the argument, and make the various parts independent of one another. A complete proof of the Geometrisation Conjecture is given, modulo pre-Perelman results on Ricci flow, Perelmans results on the -functional and \-solutions, as well as the Colding-Minicozzi extinction paper. The book can be read by anyone already familiar with these results, or willing to accept them as black boxes. The structure of the proof is presented in a lengthy introduction, which does not require knowledge of geometric analysis. The bulk of the proof is the existence theorem for Ricci flow with bubbling-off, which is treated in parts I and II. Part III deals with the long time behaviour of Ricci flow with bubbling-off. Part IV finishes the proof of the Geometrisation Conjecture. Topology bicssc Differential & Riemannian geometry bicssc Differential & Riemannian geometry bicssc Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes msc General geometric structures on low-dimensional manifolds msc Besson aut Boileau aut Maillot aut Porti aut https://ems.press/doi/10.4171/082 cover image https://content.ems.press/assets/public/images/books/cover-87.png nam a22 5a 4500 10.4171/087 DE-4084 2010-12-01 a fot 00| 0| cr nn mmmmamaa 101201e20101201gw fot 00| 0|eng d 9783037195871 10.4171/087 doi DE-4084 PBM bicssc PBX bicssc PBX bicssc 01-02 msc 51-02 msc 01A55 msc 51-01 msc 51-03 msc 53-02 msc 53-01 msc 53-03 msc 53A35 msc Papadopoulos edt Nikolai I. Lobachevsky, Pangeometry. EMS Press 2010 1 online resource (322 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 4 2523-5222 Restricted to subscribers. https://ems.press/books Lobachevsky wrote his _Pangeometry_ in 1855, the year before his death. This memoir is a résumé of his work on non-Euclidean geometry and its applications, and it can be considered as his clearest account on the subject. It is also the conclusion of his lifework, and the last attempt he made to acquire recognition. The treatise contains basic ideas of hyperbolic geometry, including the trigonometric formulae, the techniques of computation of arc length, of area and of volume, with concrete examples. It also deals with the applications of hyperbolic geometry to the computation of new definite integrals. The techniques are different from those found in most modern books on hyperbolic geometry since they do not use models. Besides its historical importance, Lobachevskys _Pangeometry_ is a beautiful work, written in a simple and condensed style. The material that it contains is still very alive, and reading this book will be most useful for researchers and for students in geometry and in the history of science. It can be used as a textbook, as a source book and as a repository of inspiration. The present edition provides the first complete English translation of the _Pangeometry_ that appears in print. It contains facsimiles of both the Russian and the French original versions. The translation is accompanied by notes, followed by a biography of Lobachevky and an extensive commentary. Geometry bicssc History of mathematics bicssc History of mathematics bicssc Research exposition (monographs, survey articles) pertaining to history and biography msc Research exposition (monographs, survey articles) pertaining to geometry msc History of mathematics in the 19th century msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry msc History of geometry msc Research exposition (monographs, survey articles) pertaining to differential geometry msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry msc History of differential geometry msc Non-Euclidean differential geometry msc https://ems.press/doi/10.4171/087 cover image https://content.ems.press/assets/public/images/books/cover-88.jpg nam a22 5a 4500 10.4171/007 DE-4084 2010-12-30 a fot 00| 0| cr nn mmmmamaa 101230e20101230gw fot 00| 0|eng d 9783037195079 10.4171/007 doi DE-4084 PBF bicssc 14Exx msc 14E30 msc 14Dxx msc 14J10 msc Faber edt Classification of Algebraic Varieties. EMS Press 2010 1 online resource (346 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 3 2523-5168 Restricted to subscribers. https://ems.press/books Fascinating and surprising developments are taking place in the classification of algebraic varieties. Work of Hacon and McKernan and many others is causing a wave of breakthroughs in the Minimal Model Program: we now know that for a smooth projective variety the canonical ring is finitely generated. These new results and methods are reshaping the field. Inspired by this exciting progress, the editors organized a meeting at Schiermonnikoog and invited leading experts to write papers about the recent developments. The result is the present volume, a lively testimony of the sudden advances that originate from these new ideas. This volume will be of interest to a wide range of pure mathematicians, but will appeal especially to algebraic and analytic geometers. Algebra bicssc Birational geometry msc Minimal model program (Mori theory, extremal rays) msc Families, fibrations in algebraic geometry msc Families, moduli, classification: algebraic theory msc Looijenga edt van der Geer edt https://ems.press/doi/10.4171/007 cover image https://content.ems.press/assets/public/images/books/cover-89.png nam a22 5a 4500 10.4171/091 DE-4084 2010-12-01 a fot 00| 0| cr nn mmmmamaa 101201e20101201gw fot 00| 0|eng d 9783037195918 10.4171/091 doi DE-4084 PBKS bicssc PBK bicssc 65-02 msc 65F05 msc 65N22 msc 65N38 msc 65R20 msc Börm aut Efficient Numerical Methods for Non-local Operators ; -Matrix Compression, Algorithms and Analysis. EMS Press 2010 1 online resource (441 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 14 2943-5005 Restricted to subscribers. https://ems.press/books Hierarchical matrices present an efficient way of treating dense matrices that arise in the context of integral equations, elliptic partial differential equations, and control theory. While a dense n\times n matrix in standard representation requires n^2 units of storage, a hierarchical matrix can approximate the matrix in a compact representation requiring only O(nklogn) units of storage, where k is a parameter controlling the accuracy. Hierarchical matrices have been successfully applied to approximate matrices arising in the context of boundary integral methods, to construct preconditioners for partial differential equations, to evaluate matrix functions and to solve matrix equations used in control theory. \mathcal{H}^2-matrices offer a refinement of hierarchical matrices: using a multilevel representation of submatrices, the efficiency can be significantly improved, particularly for large problems. This books gives an introduction to the basic concepts and presents a general framework that can be used to analyze the complexity and accuracy of \mathcal{H}^2-matrix techniques. Starting from basic ideas of numerical linear algebra and numerical analysis, the theory is developed in a straightforward and systematic way, accessible to advanced students and researchers in numerical mathematics and scientific computing. Special techniques are only required in isolated sections, e.g., for certain classes of model problems. Corrected 2nd printing, September 2013. Numerical analysis bicssc Calculus & mathematical analysis bicssc Research exposition (monographs, survey articles) pertaining to numerical analysis msc Direct numerical methods for linear systems and matrix inversion msc Numerical solution of discretized equations for boundary value problems involving PDEs msc Boundary element methods for boundary value problems involving PDEs msc Numerical methods for integral equations msc https://ems.press/doi/10.4171/091 cover image https://content.ems.press/assets/public/images/books/cover-90.png nam a22 5a 4500 10.4171/080 DE-4084 2011-02-25 a fot 00| 0| cr nn mmmmamaa 110225e20110225gw fot 00| 0|eng d 9783037195802 10.4171/080 doi DE-4084 PB bicssc 22-02 msc 22E46 msc 53C35 msc 22E50 msc 47G10 msc 32M15 msc 51N30 msc 14K25 msc 47B50 msc Neretin aut Lectures on Gaussian Integral Operators and Classical Groups. EMS Press 2011 1 online resource (571 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 13 2523-5184 Restricted to subscribers. https://ems.press/books This book is an elementary self-contained introduction to some constructions of representation theory and related topics of differential geometry and analysis. Topics covered include the theory of various Fourier-like integral operators as Segal-Bargmann transforms, Gaussian integral operators in L^2 and in the Fock space, integral operators with theta-kernels, the geometry of real and p\-adic classical groups and symmetric spaces. The heart of the book is the Weil representation of the symplectic group (real and complex realizations, relations with theta-functions and modular forms, p\-adic and adelic constructions) and representations in Hilbert spaces of holomorphic functions of several complex variables. The book is addressed to graduate students and researchers in representation theory, differential geometry, and operator theory. The reader is supposed to be familiar with standard university courses in linear algebra, functional analysis, and complex analysis. Mathematics bicssc Research exposition (monographs, survey articles) pertaining to topological groups msc Semisimple Lie groups and their representations msc Differential geometry of symmetric spaces msc Representations of Lie and linear algebraic groups over local fields msc Integral operators msc Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) msc Geometry of classical groups msc Theta functions and abelian varieties msc Linear operators on spaces with an indefinite metric msc https://ems.press/doi/10.4171/080 cover image https://content.ems.press/assets/public/images/books/cover-91.png nam a22 5a 4500 10.4171/092 DE-4084 2011-03-29 a fot 00| 0| cr nn mmmmamaa 110329e20110329gw fot 00| 0|eng d 9783037195925 10.4171/092 doi DE-4084 PBX bicssc 01-02 msc 01A40 msc 01A45 msc 01A50 msc Stedall aut From Cardanos great art to Lagranges reflections: filling a gap in the history of algebra. EMS Press 2011 1 online resource (236 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 5 2523-5222 Restricted to subscribers. https://ems.press/books This book is an exploration of a claim made by Lagrange in the autumn of 1771 as he embarked upon his lengthy Réflexions sur la résolution algébrique des équations: that there had been few advances in the algebraic solution of equations since the time of Cardano in the mid sixteenth century. That opinion has been shared by many later historians. The present study attempts to redress that view and to examine the intertwined developments in the theory of equations from Cardano to Lagrange. A similar historical exploration led Lagrange himself to insights that were to transform the entire nature and scope of algebra. Progress was not confined to any one country: at different times mathematicians in Italy, France, the Netherlands, England, Scotland, Russia, and Germany contributed to the discussion and to a gradual deepening of understanding. In particular, the national Academies of Berlin, St Petersburg, and Paris in the eighteenth century were crucial in supporting informed mathematical communities and encouraging the wider dissemination of key ideas. This study therefore truly highlights the existence of a European mathematical heritage. The book is written in three parts. Part I offers an overview of the period from Cardano to Newton (from 1545 to 1707) and is arranged chronologically. Part II covers the period from Newton to Lagrange (from 1707 to 1770) and treats the material according to key themes. Part III is a brief account of the aftermath of the discoveries made in the 1770s. The book attempts throughout to capture the reality of mathematical discovery by inviting the reader to follow in the footsteps of the authors themselves, with as few changes as possible to the original notation and style of presentation. History of mathematics bicssc Research exposition (monographs, survey articles) pertaining to history and biography msc History of mathematics in the 15th and 16th centuries, Renaissance msc History of mathematics in the 17th century msc History of mathematics in the 18th century msc https://ems.press/doi/10.4171/092 cover image https://content.ems.press/assets/public/images/books/cover-92.jpg nam a22 5a 4500 10.4171/096 DE-4084 2011-06-11 a fot 00| 0| cr nn mmmmamaa 110611e20110611gw fot 00| 0|eng d 9783037195963 10.4171/096 doi DE-4084 PB bicssc 13D03 msc 17B56 msc 14F43 msc Calaque aut Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry. EMS Press 2011 1 online resource (114 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 14 2523-5184 Restricted to subscribers. https://ems.press/books Duflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of Harish-Chandra on semi-simple Lie algebras. Later on, Duflos result was refound by Kontsevich in the framework of deformation quantization, who also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. The present book, which arose from a series of lectures by the first author at ETH, derives these two isomorphisms from a Duflo-type result for Q\-manifolds. All notions mentioned above are introduced and explained in the book, the only prerequisites being basic linear algebra and differential geometry. In addition to standard notions such as Lie (super)algebras, complex manifolds, Hochschild and Chevalley-Eilenberg cohomologies, spectral sequences, Atiyah and Todd classes, the graphical calculus introduced by Kontsevich in his seminal work on deformation quantization is addressed in details. The book is well-suited for graduate students in mathematics and mathematical physics as well as for researchers working in Lie theory, algebraic geometry and deformation theory. Mathematics bicssc (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) msc Cohomology of Lie (super)algebras msc Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) msc Rossi aut https://ems.press/doi/10.4171/096 cover image https://content.ems.press/assets/public/images/books/cover-93.png nam a22 5a 4500 10.4171/008 DE-4084 2011-07-06 a fot 00| 0| cr nn mmmmamaa 110706e20110706gw fot 00| 0|eng d 9783037195086 10.4171/008 doi DE-4084 PBK bicssc 58B34 msc 11M55 msc 11G09 msc 11M06 msc 11M32 msc 47G30 msc 81Q30 msc 81T15 msc 17A30 msc 16T30 msc 46L80 msc 46L87 msc 19K33 msc 19K56 msc 58J42 msc 58J20 msc Carey edt Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory. EMS Press 2011 1 online resource (280 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda ESI Lectures in Mathematics and Physics (esi) 8 2943-4939 Restricted to subscribers. https://ems.press/books This collection of expository articles grew out of the workshop Number Theory and Physics held in March 2009 at the The Erwin Schrödinger International Institute for Mathematical Physics, Vienna. The common theme of the articles is the influence of ideas from noncommutative geometry (NCG) on subjects ranging from number theory to Lie algebras, index theory, and mathematical physics. Matilde Marcollis article gives a survey of relevant aspects of NCG in number theory, building on an introduction to motives for beginners by Jorge Plazas and Sujatha Ramdorai. A mildly unconventional view of index theory from the viewpoint of NCG is described in the article by Alan Carey, John Phillips and Adam Rennie. As developed by Alain Connes and Dirk Kreimer, NCG also provides insight into novel algebraic structures underlying many analytic aspects of quantum field theory. Dominique Manchon's article on pre-Lie algebras fits into this developing research area. This interplay of algebraic and analytic techniques also appears in the articles by Christoph Bergbauer, who introduces renormalisation theory and Feynman diagram methods, and Sylvie Paycha, who focuses on relations between renormalisation and zeta function techniques. Calculus & mathematical analysis bicssc Noncommutative geometry (à la Connes) msc Relations with noncommutative geometry msc Drinfel'd modules; higher-dimensional motives, etc. msc \(\zeta (s)\) and \(L(s, \chi)\) msc Multiple Dirichlet series and zeta functions and multizeta values msc Pseudodifferential operators msc Feynman integrals and graphs; applications of algebraic topology and algebraic geometry msc Perturbative methods of renormalization applied to problems in quantum field theory msc Nonassociative algebras satisfying other identities msc Connections of Hopf algebras with combinatorics msc \(K\)-theory and operator algebras (including cyclic theory) msc Noncommutative differential geometry msc Ext and \(K\)-homology msc Index theory msc Noncommutative global analysis, noncommutative residues msc Index theory and related fixed-point theorems on manifolds msc https://ems.press/doi/10.4171/008 cover image https://content.ems.press/assets/public/images/books/cover-95.png nam a22 5a 4500 10.4171/083 DE-4084 2011-08-11 a fot 00| 0| cr nn mmmmamaa 110811e20110811gw fot 00| 0|eng d 9783037195833 10.4171/083 doi DE-4084 PBPD bicssc 55-02 msc 18B40 msc 18G50 msc 55P15 msc 18A30 msc 18A40 msc 18D15 msc 18D30 msc 19D23 msc 20F65 msc 20L05 msc 55Q45 msc 55S37 msc 55S45 msc 55U10 msc 55U15 msc 55U35 msc 57M05 msc 57M10 msc 57M15 msc Brown aut Nonabelian Algebraic Topology ; Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids. EMS Press 2011 1 online resource (703 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 15 2943-5005 Restricted to subscribers. https://ems.press/books The main theme of this book is that the use of filtered spaces rather than just topological spaces allows the development of basic algebraic topology in terms of higher homotopy groupoids; these algebraic structures better reflect the geometry of subdivision and composition than those commonly in use. Exploration of these uses of higher dimensional versions of groupoids has been largely the work of the first two authors since the mid 1960s. The structure of the book is intended to make it useful to a wide class of students and researchers for learning and evaluating these methods, primarily in algebraic topology but also in higher category theory and its applications in analogous areas of mathematics, physics and computer science. Part I explains the intuitions and theory in dimensions 1 and 2, with many figures and diagrams, and a detailed account of the theory of crossed modules. Part II develops the applications of crossed complexes. The engine driving these applications is the work of Part III on cubical -groupoids, their relations to crossed complexes, and their homotopically defined examples for filtered spaces. Part III also includes a chapter suggesting further directions and problems, and three appendices give accounts of some relevant aspects of category theory. Endnotes for each chapter give further history and references. Algebraic topology bicssc Research exposition (monographs, survey articles) pertaining to algebraic topology msc Groupoids, semigroupoids, semigroups, groups (viewed as categories) msc Nonabelian homological algebra (category-theoretic aspects) msc Classification of homotopy type msc Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) msc Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) msc Closed categories (closed monoidal and Cartesian closed categories, etc.) msc Fibered categories msc Symmetric monoidal categories msc Geometric group theory msc Groupoids (i.e. small categories in which all morphisms are isomorphisms) msc Stable homotopy of spheres msc Classification of mappings in algebraic topology msc Postnikov systems, \(k\)-invariants msc Simplicial sets and complexes in algebraic topology msc Chain complexes in algebraic topology msc Abstract and axiomatic homotopy theory in algebraic topology msc Fundamental group, presentations, free differential calculus msc Covering spaces and low-dimensional topology msc Relations of low-dimensional topology with graph theory msc Higgins aut Sivera aut https://ems.press/doi/10.4171/083 cover image https://content.ems.press/assets/public/images/books/cover-96.png nam a22 5a 4500 10.4171/098 DE-4084 2011-08-11 a fot 00| 0| cr nn mmmmamaa 110811e20110811gw fot 00| 0|eng d 9783037195987 10.4171/098 doi DE-4084 PBK bicssc 32-02 msc 32D15 msc 32A10 msc 32A17 msc 32D05 msc 32D10 msc 32D26 msc 32U15 msc Jarnicki aut Separately Analytic Functions. EMS Press 2011 1 online resource (306 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 16 2943-5005 Restricted to subscribers. https://ems.press/books The story of separately holomorphic functions began about 100 years ago. During the second half of the 19th century, it became known that a separately continuous function is not necessarily continuous as a function of all variables. At the beginning of the 20th century, the study of separately holomorphic functions started due to the fundamental work of Osgood and Hartogs. This book provides the first self-contained and complete presentation of the study of separately holomorphic functions, starting from its birth up to current research. Most of the results presented have never been published before in book form. The text is divided into two parts. A more elementary one deals with separately holomorphic functions without singularities, another addresses the situation of existing singularities. A discussion of the classical results related to separately holomorphic functions leads to the most fundamental result, the classical cross theorem as well as various extensions and generalizations to more complicated crosses. Additionally, several applications for other classes of separately regular functions are given. A solid background in basic complex analysis is a prerequisite. In order to make the book self-contained, all the results needed for its understanding are collected in special introductory chapters and referred to at the beginning of each section. The book is addressed to students and researchers in several complex variables as well as to mathematicians and theoretical physicists who are interested in this area of mathematics. Calculus & mathematical analysis bicssc Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces msc Continuation of analytic objects in several complex variables msc Holomorphic functions of several complex variables msc Special families of functions of several complex variables msc Domains of holomorphy msc Envelopes of holomorphy msc Riemann domains msc General pluripotential theory msc Pflug aut https://ems.press/doi/10.4171/098 cover image https://content.ems.press/assets/public/images/books/cover-94.png nam a22 5a 4500 10.4171/097 DE-4084 2011-08-06 a fot 00| 0| cr nn mmmmamaa 110806e20110806gw fot 00| 0|eng d 9783037195970 10.4171/097 doi DE-4084 PBK bicssc 58-02 msc 58A50 msc 58C50 msc 14M30 msc 17A70 msc 32C11 msc 81Q60 msc Carmeli aut Mathematical Foundations of Supersymmetry. EMS Press 2011 1 online resource (300 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 15 2523-5184 Restricted to subscribers. https://ems.press/books Supersymmetry is a highly active area of considerable interest among physicists and mathematicians. It is not only fascinating in its own right, but there is also indication that it plays a fundamental role in the physics of elementary particles and gravitation. The purpose of the book is to lay down the foundations of the subject, providing the reader with a comprehensive introduction to the language and techniques, with a special attention to giving detailed proofs and many clarifying examples. It is aimed ideally at a second year graduate student. After the first three introductory chapters, the text divides into two parts: the theory of smooth supermanifolds and Lie supergroups, including the Frobenius theorem, and the theory of algebraic superschemes and supergroups. There are three appendices, the first introducing Lie superalgebras and representations of classical Lie superalgebras, the second collecting some relevant facts on categories, sheafification of functors and commutative algebra, and the third explaining the notion of Fréchet space in the super context. Calculus & mathematical analysis bicssc Research exposition (monographs, survey articles) pertaining to global analysis msc Supermanifolds and graded manifolds msc Analysis on supermanifolds or graded manifolds msc Supervarieties msc Superalgebras msc Complex supergeometry msc Supersymmetry and quantum mechanics msc Caston aut Fioresi aut https://ems.press/doi/10.4171/097 cover image https://content.ems.press/assets/public/images/books/cover-97.png nam a22 5a 4500 10.4171/072 DE-4084 2011-08-10 a fot 00| 0| cr nn mmmmamaa 110810e20110810gw fot 00| 0|eng d 9783037195727 10.4171/072 doi DE-4084 PBWL bicssc 60-06 msc 60Gxx msc 60Jxx msc Blath edt Surveys in Stochastic Processes. EMS Press 2011 1 online resource (263 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 4 2523-5168 Restricted to subscribers. https://ems.press/books The 33rd Bernoulli Society Conference on Stochastic Processes and Their Applications was held in Berlin from July 27 to July 31, 2009. It brought together more than 600 researchers from 49 countries, who communicated recent progress in the mathematical research related to stochastic processes, with applications ranging from biology to statistical mechanics, finance and climatology. The present book collects survey articles highlighting new trends and focal points in the area written by plenary speakers of the conference, all of them outstanding international experts. A particular aim of this collection is to inspire young scientists in setting up research goals within the wide scope of fields represented in this volume. Stochastics bicssc Proceedings, conferences, collections, etc. pertaining to probability theory msc Stochastic processes msc Markov processes msc Imkeller edt Rlly edt https://ems.press/doi/10.4171/072 cover image https://content.ems.press/assets/public/images/books/cover-98.jpg nam a22 5a 4500 10.4171/095 DE-4084 2011-09-02 a fot 00| 0| cr nn mmmmamaa 110902e20110902gw fot 00| 0|eng d 9783037195956 10.4171/095 doi DE-4084 PBKJ bicssc 35L70 msc 35Q55 msc 37D10 msc 37K40 msc 37K45 msc Nakanishi aut Invariant Manifolds and Dispersive Hamiltonian Evolution Equations. EMS Press 2011 1 online resource (258 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 14 2943-4971 Restricted to subscribers. https://ems.press/books The notion of an invariant manifold arises naturally in the asymptotic stability analysis of stationary or standing wave solutions of unstable dispersive Hamiltonian evolution equations such as the focusing semilinear Klein-Gordon and Schrödinger equations. This is due to the fact that the linearized operators about such special solutions typically exhibit negative eigenvalues (a single one for the ground state), which lead to exponential instability of the linearized flow and allows for ideas from hyperbolic dynamics to enter. One of the main results proved here for energy subcritical equations is that the center-stable manifold associated with the ground state appears as a hyper-surface which separates a region of finite-time blowup in forward time from one which exhibits global existence and scattering to zero in forward time. Our entire analysis takes place in the energy topology, and the conserved energy can exceed the ground state energy only by a small amount. This monograph is based on recent research by the authors and the proofs rely on an interplay between the variational structure of the ground states on the one hand, and the nonlinear hyperbolic dynamics near these states on the other hand. A key element in the proof is a virial-type argument excluding almost homoclinic orbits originating near the ground states, and returning to them, possibly after a long excursion. These lectures are suitable for graduate students and researchers in partial differential equations and mathematical physics. For the cubic Klein-Gordon equation in three dimensions all details are provided, including the derivation of Strichartz estimates for the free equation and the concentration-compactness argument leading to scattering due to Kenig and Merle. Differential calculus & equations bicssc Second-order nonlinear hyperbolic equations msc NLS equations (nonlinear Schrödinger equations) msc Invariant manifold theory for dynamical systems msc Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems msc Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems msc Schlag aut https://ems.press/doi/10.4171/095 cover image https://content.ems.press/assets/public/images/books/cover-99.png nam a22 5a 4500 10.4171/101 DE-4084 2011-09-24 a fot 00| 0| cr nn mmmmamaa 110924e20110924gw fot 00| 0|eng d 9783037196014 10.4171/101 doi DE-4084 PB bicssc 13Dxx msc 13Fxx msc 14Bxx msc 14Hxx msc 14Lxx msc 14Mxx msc 14Nxx msc 15Axx msc 16Dxx msc 16Exx msc 16Gxx msc 16Sxx msc 16Wxx msc 17Bxx msc 18Exx msc 19Kxx msc 20Cxx msc 20Jxx msc Skowroński edt Representations of Algebras and Related Topics. EMS Press 2011 1 online resource (740 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 5 2523-5168 Restricted to subscribers. https://ems.press/books This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, combinatorics, quantum algebras, and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, Calabi-Yau algebras and categories, triangulated and derived categories, quantum loop algebras, Nakajima quiver varieties, Yang-Baxter equations, T\-systems and Y\-systems, dilogarithm and quantum dilogarithm identities, stable module categories, localizing and colocalizing subcategories, cohomologies of groups, support varieties, fusion systems, Hochschild cohomologies, weighted projective lines, coherent sheaves, Kleinian and Fuchsian singularities, stable categories of vector bundles, nilpotent operators, Artin-Schelter regular algebras, Fano algebras, deformations of algebras, module varieties, degenerations of modules, singularities of orbit closures, coalgebras and comodules, representation types of algebras and coalgebras, Tits and Euler forms of algebras, Galois coverings of algebras, tilting and cluster tilting theory, algebras of small homological dimensions, Auslander-Reiten theory. The book consists of thirteen self-contained expository survey and research articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of examples and open problems and give new perspectives for research in the field. Mathematics bicssc Homological methods in commutative ring theory msc Arithmetic rings and other special commutative rings msc Local theory in algebraic geometry msc Curves in algebraic geometry msc Algebraic groups msc Special varieties msc Projective and enumerative algebraic geometry msc Basic linear algebra msc Modules, bimodules and ideals in associative algebras msc Homological methods in associative algebras msc Representation theory of associative rings and algebras msc Associative rings and algebras arising under various constructions msc Associative rings and algebras with additional structure msc Lie algebras and Lie superalgebras msc Categorical algebra msc \(K\)-theory and operator algebras msc Representation theory of groups msc Connections of group theory with homological algebra and category theory msc Yamagata edt https://ems.press/doi/10.4171/101 cover image https://content.ems.press/assets/public/images/books/cover-103.jpg nam a22 5a 4500 10.4171/088 DE-4084 2011-09-25 a fot 00| 0| cr nn mmmmamaa 110925e20110925gw fot 00| 0|eng d 9783037195888 10.4171/088 doi DE-4084 PBCD bicssc 03-01 msc 03A05 msc 03B40 msc 18A15 msc Girard aut The Blind Spot ; Lectures on Logic. EMS Press 2011 1 online resource (550 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books These lectures on logic, more specifically proof theory, are basically intended for postgraduate students and researchers in logic. The question at stake is the nature of mathematical knowledge and the difference between a question and an answer, i.e., the implicit and the explicit. The problem is delicate mathematically and philosophically as well: the relation between a question and its answer is a sort of equality where one side is more equal than the other: one thus discovers essentialist blind spots. Starting with Gödels paradox (1931) - so to speak, the incompleteness of answers with respect to questions - the book proceeds with paradigms inherited from Gentzens cut-elimination (1935). Various settings are studied: sequent calculus, natural deduction, lambda calculi, category-theoretic composition, up to geometry of interaction (GoI), all devoted to explicitation, which eventually amounts to inverting an operator in a von Neumann algebra. Mathematical language is usually described as referring to a preexisting reality. Logical operations can be given an alternative procedural meaning: typically, the operators involved in GoI are invertible, not because they are constructed according to the book, but because logical rules are those ensuring invertibility. Similarly, the durability of truth should not be taken for granted: one should distinguish between imperfect (perennial) and perfect modes. The procedural explanation of the infinite thus identifies it with the unfinished, i.e., the perennial. But is perenniality perennial? This questioning yields a possible logical explanation for algorithmic complexity. This highly original course on logic by one of the worlds leading proof theorists challenges mathematicians, computer scientists, physicists and philosophers to rethink their views and concepts on the nature of mathematical knowledge in an exceptionally profound way. Mathematical logic bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations msc Philosophical and critical aspects of logic and foundations msc Combinatory logic and lambda calculus msc Foundations, relations to logic and deductive systems msc https://ems.press/doi/10.4171/088 cover image https://content.ems.press/assets/public/images/books/cover-101.png nam a22 5a 4500 10.4171/104 DE-4084 2011-10-20 a fot 00| 0| cr nn mmmmamaa 111020e20111020gw fot 00| 0|eng d 9783037196045 10.4171/104 doi DE-4084 PBX bicssc 01-02 msc 01A75 msc 00B55 msc 11-03 msc 11A55 msc 12-03 msc 12E12 msc 12E20 msc 12F10 msc 20-02 msc 20-03 msc 20B05 msc 20B15 msc 20D05 msc 33-03 msc 33E05 msc Neumann aut The mathematical writings of Évariste Galois ; Corrected 2nd printing, September 2013. EMS Press 2011 1 online resource (421 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 6 2523-5222 Restricted to subscribers. https://ems.press/books Although Évariste Galois was only 20 years old when he died, shot in a mysterious early-morning duel in 1832, his ideas, when they were published 14 years later, changed the course of algebra. He invented what is now called Galois Theory, the modern form of what was classically the Theory of Equations. For that purpose, and in particular to formulate a precise condition for solubility of equations by radicals, he also invented groups and began investigating their theory. His main writings were published in French in 1846 and there have been a number of French editions culminating in the great work published by Bourgne & Azra in 1962 containing transcriptions of every page and fragment of the manuscripts that survive. Very few items have been available in English up to now. The present work contains English translations of almost all the Galois material. They are presented alongside a new transcription of the original French, and are enhanced by three levels of commentary. An introduction explains the context of Galois' work, the various publications in which it appears, and the vagaries of his manuscripts. Then there is a chapter in which the five mathematical articles published in his lifetime are reprinted. After that come the Testamentary Letter and the First Memoir (in which Galois expounded the ideas now called Galois Theory), which are the most famous of the manuscripts. There follow the less well known manuscripts, namely the Second Memoir and the many fragments. A short epilogue devoted to myths and mysteries concludes the text. The book is written as a contribution to the history of mathematics but with mathematicans as well as historians in mind. It makes available to a wide mathematical and historical readership some of the most exciting mathematics of the first half of the 19th century, presented in its original form. The primary aim is to establish a text of what Galois wrote. Exegesis would fill another book or books, and little of that is to be found here. This work will be a resource for research in the history of mathematics, especially algebra, as well as a sourcebook for those many mathematicians who enliven their student lectures with reliable historical background. History of mathematics bicssc Research exposition (monographs, survey articles) pertaining to history and biography msc Collected or selected works; reprintings or translations of classics msc Collections of translated articles of miscellaneous specific interest msc History of number theory msc Continued fractions msc History of field theory msc Equations in general fields msc Finite fields (field-theoretic aspects) msc Separable extensions, Galois theory msc Research exposition (monographs, survey articles) pertaining to group theory msc History of group theory msc General theory for finite permutation groups msc Primitive groups msc Finite simple groups and their classification msc History of special functions msc Elliptic functions and integrals msc https://ems.press/doi/10.4171/104 cover image https://content.ems.press/assets/public/images/books/cover-102.jpg nam a22 5a 4500 10.4171/099 DE-4084 2011-11-05 a fot 00| 0| cr nn mmmmamaa 111105e20111105gw fot 00| 0|eng d 9783037195994 10.4171/099 doi DE-4084 PBK bicssc 31-02 msc 31E05 msc 28A12 msc 30L99 msc 31C05 msc 31C15 msc 31C40 msc 31C45 msc 35B45 msc 35B65 msc 35D30 msc 35J20 msc 35J25 msc 35J60 msc 35J67 msc 35J70 msc 35J92 msc 46E35 msc 47J20 msc 49J10 msc 49J27 msc 49J40 msc 49J52 msc 49N60 msc 49Q20 msc 58C99 msc 58J05 msc 58J32 msc Björn aut Nonlinear Potential Theory on Metric Spaces. EMS Press 2011 1 online resource (415 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 17 2943-5005 Restricted to subscribers. https://ems.press/books The p\-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory and image processing. Its solutions, called p\-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs and Heisenberg groups. Nonlinear potential theory of p\-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories. This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for an interested reader and as a reference text for an active researcher. The presentation is rather self-contained, but the reader is assumed to know measure theory and functional analysis. The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p\-harmonic functions on metric spaces and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space. Each chapter contains historical notes with relevant references and an extensive index is provided at the end of the book. Calculus & mathematical analysis bicssc Research exposition (monographs, survey articles) pertaining to potential theory msc Potential theory on fractals and metric spaces msc Contents, measures, outer measures, capacities msc Analysis on metric spaces msc Harmonic, subharmonic, superharmonic functions on other spaces msc Potentials and capacities on other spaces msc Fine potential theory; fine properties of sets and functions msc Other generalizations (nonlinear potential theory, etc.) msc A priori estimates in context of PDEs msc Smoothness and regularity of solutions to PDEs msc Weak solutions to PDEs msc Variational methods for second-order elliptic equations msc Boundary value problems for second-order elliptic equations msc Nonlinear elliptic equations msc Boundary values of solutions to elliptic equations and elliptic systems msc Degenerate elliptic equations msc Quasilinear elliptic equations with \(p\)-Laplacian msc Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems msc Variational and other types of inequalities involving nonlinear operators (general) msc Existence theories for free problems in two or more independent variables msc Existence theories for problems in abstract spaces msc Variational inequalities msc Nonsmooth analysis msc Regularity of solutions in optimal control msc Variational problems in a geometric measure-theoretic setting msc Calculus on manifolds; nonlinear operators msc Elliptic equations on manifolds, general theory msc Boundary value problems on manifolds msc Björn aut https://ems.press/doi/10.4171/099 cover image https://content.ems.press/assets/public/images/books/cover-100.png nam a22 5a 4500 10.4171/102 DE-4084 2011-12-13 a fot 00| 0| cr nn mmmmamaa 111213e20111213gw fot 00| 0|eng d 9783037196021 10.4171/102 doi DE-4084 PB bicssc 16-01 msc 13E10 msc 15A63 msc 15A69 msc 16Dxx msc 16E30 msc 16G10 msc 16G20 msc 16G70 msc 16K20 msc 51F15 msc Skowroński aut Frobenius Algebras I ; Basic Representation Theory. EMS Press 2011 1 online resource (661 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 11 2943-4955 Restricted to subscribers. https://ems.press/books This is the first of two volumes which will provide a comprehensive introduction to the modern representation theory of Frobenius algebras. The first part of the book serves as a general introduction to basic results and techniques of the modern representation theory of finite dimensional associative algebras over fields, including the Morita theory of equivalences and dualities and the Auslander-Reiten theory of irreducible morphisms and almost split sequences. The second part is devoted to fundamental classical and recent results concerning the Frobenius algebras and their module categories. Moreover, the prominent classes of Frobenius algebras, the Hecke algebras of Coxeter groups and the finite dimensional Hopf algebras over fields are exhibited. This volume is self-contained and the only prerequisite is a basic knowledge of linear algebra. It includes complete proofs of all results presented and provides a rich supply of examples and exercises. The text is primarily addressed to graduate students starting research in the representation theory of algebras as well mathematicians working in other fields. Mathematics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras msc Commutative Artinian rings and modules, finite-dimensional algebras msc Quadratic and bilinear forms, inner products msc Multilinear algebra, tensor calculus msc Modules, bimodules and ideals in associative algebras msc Homological functors on modules (Tor, Ext, etc.) in associative algebras msc Representations of associative Artinian rings msc Representations of quivers and partially ordered sets msc Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers msc Finite-dimensional division rings msc Reflection groups, reflection geometries msc Yamagata aut https://ems.press/doi/10.4171/102 cover image https://content.ems.press/assets/public/images/books/cover-105.png nam a22 5a 4500 10.4171/100 DE-4084 2012-01-14 a fot 00| 0| cr nn mmmmamaa 120114e20120114gw fot 00| 0|eng d 9783037196007 10.4171/100 doi DE-4084 PB bicssc 65P10 msc 37M15 msc 35Q41 msc Faou aut Geometric Numerical Integration and Schrödinger Equations. EMS Press 2012 1 online resource (146 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 15 2943-4971 Restricted to subscribers. https://ems.press/books The goal of geometric numerical integration is the simulation of evolution equations possessing geometric properties over long times. Of particular importance are Hamiltonian partial differential equations typically arising in application fields such as quantum mechanics or wave propagation phenomena. They exhibit many important dynamical features such as energy preservation and conservation of adiabatic invariants over long time. In this setting, a natural question is how and to which extent the reproduction of such long time qualitative behavior can be ensured by numerical schemes. Starting from numerical examples, these notes provide a detailed analysis of the Schrödinger equation in a simple setting (periodic boundary conditions, polynomial nonlinearities) approximated by symplectic splitting methods. Analysis of stability and instability phenomena induced by space and time discretization are given, and rigorous mathematical explanations for them. The book grew out of a graduate level course and is of interest to researchers and students seeking an introduction to the subject matter. Mathematics bicssc Numerical methods for Hamiltonian systems including symplectic integrators msc Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems msc Time-dependent Schrödinger equations and Dirac equations msc https://ems.press/doi/10.4171/100 cover image https://content.ems.press/assets/public/images/books/cover-104.jpg nam a22 5a 4500 10.4171/075 DE-4084 2012-01-02 a fot 00| 0| cr nn mmmmamaa 120102e20120102gw fot 00| 0|eng d 9783037195758 10.4171/075 doi DE-4084 PBKD bicssc 30-02 msc 30F60 msc 32G15 msc 30F10 msc 30Fxx msc Penner aut Decorated Teichmüller Theory. EMS Press 2012 1 online resource (377 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda The QGM Master Class Series (qgm) 1 Restricted to subscribers. https://ems.press/books There is an essentially tinker-toy model of a trivial bundle over the classical Teichmüller space of a punctured surface, called the decorated Teichmüller space, where the fiber over a point is the space of all tuples of horocycles, one about each puncture. This model leads to an extension of the classical mapping class groups called the Ptolemy groupoids and to certain matrix models solving related enumerative problems, each of which has proved useful both in mathematics and in theoretical physics. These spaces enjoy several related parametrizationsleading to a rich and intricate algebro-geometric structure tied to the already elaborate combinatorial structure of the tinker-toy model. Indeed, the natural coordinates give the prototypical examples not only of cluster algebras but also of tropicalization. This interplay of combinatorics and coordinates admits further manifestations, for example, in a Lie theory for homeomorphisms of the circle, in the geometry underlying the Gauss product, in profinite and pronilpotent geometry, in the combinatorics underlying conformal and topological quantum field theories, and in the geometry and combinatorics of macromolecules. This volume gives the story and wider context of these decorated Teichmüller spaces as developed by the author over the last two decades in a series of papers, some of them in collaboration. Sometimes correcting errors or typos, sometimes simplifying proofs and sometimes articulating more general formulations than the original research papers, this volume is self-contained and requires little formal background. Based on a masters course at Aarhus University, it gives the first treatment of these works in monographic form. Complex analysis, complex variables bicssc Research exposition (monographs, survey articles) pertaining to functions of a complex variable msc Teichmüller theory for Riemann surfaces msc Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) msc Compact Riemann surfaces and uniformization msc Riemann surfaces msc https://ems.press/doi/10.4171/075 cover image https://content.ems.press/assets/public/images/books/cover-106.jpg nam a22 5a 4500 10.4171/105 DE-4084 2012-01-18 a fot 00| 0| cr nn mmmmamaa 120118e20120118gw fot 00| 0|eng d 9783037196052 10.4171/105 doi DE-4084 PBM bicssc 51-01 msc 51-02 msc 57-01 msc 57-02 msc 14H30 msc 14H52 msc 20F67 msc 20F69 msc 22E40 msc 22D40 msc 30F10 msc 30F20 msc 30F45 msc 30F60 msc 32G15 msc 37E30 msc 51F99 msc 51M10 msc 51E24 msc 53C21 msc 53C22 msc 53C23 msc 53C35 msc 53C70 msc 54C20 msc 57M15 msc 57M50 msc Papadopoulos edt Strasbourg Master Class on Geometry. EMS Press 2012 1 online resource (461 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 18 2523-5141 Restricted to subscribers. https://ems.press/books This book contains carefully revised and expanded versions of eight courses that were presented at the University of Strasbourg, during two geometry master classes, in 2008 and 2009. The aim of the master classes was to give to fifth-year students and PhD students in mathematics the opportunity to learn new topics that lead directly to the current research in geometry and topology. The courses were held by leading experts. The subjects treated include hyperbolic geometry, three-manifold topology, representation theory of fundamental groups of surfaces and of three-manifolds, dynamics on the hyperbolic plane with applications to number theory, Riemann surfaces, Teichmüller theory, Lie groups and asymptotic geometry. The text is addressed to students and mathematicians who wish to learn the subject. It can also be used as a reference book and as a textbook for short courses on geometry. Geometry bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry msc Research exposition (monographs, survey articles) pertaining to geometry msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes msc Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes msc Coverings of curves, fundamental group msc Elliptic curves msc Hyperbolic groups and nonpositively curved groups msc Asymptotic properties of groups msc Discrete subgroups of Lie groups msc Ergodic theory on groups msc Compact Riemann surfaces and uniformization msc Classification theory of Riemann surfaces msc Conformal metrics (hyperbolic, Poincaré, distance functions) msc Teichmüller theory for Riemann surfaces msc Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) msc Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces msc Metric geometry msc Hyperbolic and elliptic geometries (general) and generalizations msc Buildings and the geometry of diagrams msc Methods of global Riemannian geometry, including PDE methods; curvature restrictions msc Geodesics in global differential geometry msc Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces msc Differential geometry of symmetric spaces msc Direct methods (\(G\)-spaces of Busemann, etc.) msc Extension of maps msc Relations of low-dimensional topology with graph theory msc General geometric structures on low-dimensional manifolds msc https://ems.press/doi/10.4171/105 cover image https://content.ems.press/assets/public/images/books/cover-107.png nam a22 5a 4500 10.4171/106 DE-4084 2012-02-09 a fot 00| 0| cr nn mmmmamaa 120209e20120209gw fot 00| 0|eng d 9783037196069 10.4171/106 doi DE-4084 PBKJ bicssc PBMP bicssc 35L05 msc 35L52 msc 53Z05 msc Krieger aut Concentration Compactness for Critical Wave Maps. EMS Press 2012 1 online resource (490 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Monographs in Mathematics (emm) 5 2523-5206 Restricted to subscribers. https://ems.press/books Wave maps are the simplest wave equations taking their values in a Riemannian manifold (M,g). Their Lagrangian is the same as for the scalar equation, the only difference being that lengths are measured with respect to the metric g. By Noether's theorem, symmetries of the Lagrangian imply conservation laws for wave maps, such as conservation of energy. In coordinates, wave maps are given by a system of semilinear wave equations. Over the past 20 years important methods have emerged which address the problem of local and global wellposedness of this system. Due to weak dispersive effects, wave maps defined on Minkowski spaces of low dimensions, such as \mathbb R^{2+1}_{t,x}, present particular technical difficulties. This class of wave maps has the additional important feature of being energy critical, which refers to the fact that the energy scales exactly like the equation. Around 2000 Daniel Tataru and Terence Tao, building on earlier work of Klainerman-Machedon, proved that smooth data of small energy lead to global smooth solutions for wave maps from 2+1 dimensions into target manifolds satisfying some natural conditions. In contrast, for large data, singularities may occur in finite time for M \mathbb S^2 as target. This monograph establishes that for \mathbb H as target the wave map evolution of any smooth data exists globally as a smooth function. While we restrict ourselves to the hyperbolic plane as target the implementation of the concentration-compactness method, the most challenging piece of this exposition, yields more detailed information on the solution. This monograph will be of interest to experts in nonlinear dispersive equations, in particular to those working on geometric evolution equations. Differential calculus & equations bicssc Differential & Riemannian geometry bicssc Wave equation msc Initial value problems for second-order hyperbolic systems msc Applications of differential geometry to physics msc Schlag aut https://ems.press/doi/10.4171/106 cover image https://content.ems.press/assets/public/images/books/cover-108.jpg nam a22 5a 4500 10.4171/107 DE-4084 2012-03-16 a fot 00| 0| cr nn mmmmamaa 120316e20120316gw fot 00| 0|eng d 9783037196076 10.4171/107 doi DE-4084 PB bicssc 46-02 msc 46E35 msc 42C40 msc 42B35 msc 68Q17 msc 41A55 msc Triebel aut Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration. EMS Press 2012 1 online resource (115 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 16 2523-5184 Restricted to subscribers. https://ems.press/books This book deals first with Haar bases, Faber bases and Faber frames for weighted function spaces on the real line and the plane. It extends results in the authors book _Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration_ (EMS, 2010) from unweighted spaces (preferably in cubes) to weighted spaces. The obtained assertions are used to study sampling and numerical integration in weighted spaces on the real line and weighted spaces with dominating mixed smoothness in the plane. A short chapter deals with the discrepancy for spaces on intervals. The book is addressed to graduate students and mathematicians having a working knowledge of basic elements of function spaces and approximation theory. Mathematics bicssc Research exposition (monographs, survey articles) pertaining to functional analysis msc Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems msc Nontrigonometric harmonic analysis involving wavelets and other special systems msc Function spaces arising in harmonic analysis msc Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) msc Approximate quadratures msc https://ems.press/doi/10.4171/107 cover image https://content.ems.press/assets/public/images/books/cover-109.png nam a22 5a 4500 10.4171/108 DE-4084 2012-03-16 a fot 00| 0| cr nn mmmmamaa 120316e20120316gw fot 00| 0|eng d 9783037196083 10.4171/108 doi DE-4084 PBF bicssc 18-01 msc 17B10 msc 17B55 msc 18A40 msc Mazorchuk aut Lectures on Algebraic Categorification. EMS Press 2012 1 online resource (128 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda The QGM Master Class Series (qgm) 2 Restricted to subscribers. https://ems.press/books The term categorification was introduced by Louis Crane in 1995 and refers to the process of replacing set-theoretic notions by the corresponding category-theoretic analogues. This text mostly concentrates on algebraical aspects of the theory, presented in the historical perspective, but also contains several topological applications, in particular, an algebraic (or, more precisely, representation-theoretical) approach to categorification. It consists of fifteen sections corresponding to fifteen one-hour lectures given during a Master Class at Aarhus University, Denmark in October 2010. There are some exercises collected at the end of the text and a rather extensive list of references. Video recordings of all (but one) lectures are available from the Master Class website. The book provides an introductory overview of the subject rather than a fully detailed monograph. Emphasis is on definitions, examples and formulations of the results. Most proofs are either briefly outlined or omitted. However, complete proofs can be found by tracking references. It is assumed that the reader is familiar with the basics of category theory, representation theory, topology and Lie algebra. Algebra bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to category theory msc Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) msc Homological methods in Lie (super)algebras msc Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) msc https://ems.press/doi/10.4171/108 cover image https://content.ems.press/assets/public/images/books/cover-110.jpg nam a22 5a 4500 10.4171/109 DE-4084 2012-05-11 a fot 00| 0| cr nn mmmmamaa 120511e20120511gw fot 00| 0|eng d 9783037196090 10.4171/109 doi DE-4084 PBT bicssc 60K35 msc 60J27 msc 60G15 msc 82B41 msc Sznitman aut Topics in Occupation Times and Gaussian Free Fields. EMS Press 2012 1 online resource (121 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 16 2943-4971 Restricted to subscribers. https://ems.press/books This book grew out of a graduate course at ETH Zurich during the Spring term 2011. It explores various links between such notions as occupation times of Markov chains, Gaussian free fields, Poisson point processes of Markovian loops, and random interlacements, which have been the object of intensive research over the last few years. These notions are developed in the convenient set-up of finite weighted graphs endowed with killing measures. The book first discusses elements of continuous-time Markov chains, Dirichlet forms, potential theory, together with some consequences for Gaussian free fields. Next, isomorphism theorems and generalized Ray-Knight theorems, which relate occupation times of Markov chains to Gaussian free fields, are pre- sented. Markovian loops are constructed and some of their key properties derived. The field of occupation times of Poisson point processes of Markovian loops is investigated. Of special interest are its connection to the Gaussian free field, and a formula of Symanzik. Finally, links between random interlacements and Markovian loops are discussed, and some further connections with Gaussian free fields are mentioned. Probability & statistics bicssc Interacting random processes; statistical mechanics type models; percolation theory msc Continuous-time Markov processes on discrete state spaces msc Gaussian processes msc Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics msc https://ems.press/doi/10.4171/109 cover image https://content.ems.press/assets/public/images/books/cover-111.png nam a22 5a 4500 10.4171/110 DE-4084 2012-06-13 a fot 00| 0| cr nn mmmmamaa 120613e20120613gw fot 00| 0|eng d 9783037196106 10.4171/110 doi DE-4084 PBV bicssc 05-02 msc 20-02 msc 51-02 msc 05B25 msc 05E18 msc 20B25 msc 20D15 msc 20D20 msc 51B25 msc 51E12 msc Thas aut A Course on Elation Quadrangles. EMS Press 2012 1 online resource (129 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 17 2523-5184 Restricted to subscribers. https://ems.press/books The notion of elation generalized quadrangle is a natural generalization to the theory of generalized quadrangles of the important notion of translation planes in the theory of projective planes. Almost any known class of finite generalized quadrangles can be constructed from a suitable class of elation quadrangles. In this book the author considers several aspects of the theory of elation generalized quadrangles. Special attention is given to local Moufang conditions on the foundational level, exploring for instance a question of Knarr from the 1990s concerning the very notion of elation quadrangles. All the known results on Kantors prime power conjecture for finite elation quadrangles are gathered, some of them published here for the first time. The structural theory of elation quadrangles and their groups is heavily emphasized. Other related topics, such as p\-modular cohomology, Heisenberg groups and existence problems for certain translation nets, are briefly touched. The text starts from scratch and is essentially self-contained. Many alternative proofs are given for known theorems. Containing dozens of exercises at various levels, from very easy to rather difficult, this course will stimulate undergraduate and graduate students to enter the fascinating and rich world of elation quadrangles. The more accomplished mathematician will especially find the final chapters challenging. Combinatorics & graph theory bicssc Research exposition (monographs, survey articles) pertaining to combinatorics msc Research exposition (monographs, survey articles) pertaining to group theory msc Research exposition (monographs, survey articles) pertaining to geometry msc Combinatorial aspects of finite geometries msc Group actions on combinatorial structures msc Finite automorphism groups of algebraic, geometric, or combinatorial structures msc Finite nilpotent groups, \(p\)-groups msc Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure msc Lie geometries in nonlinear incidence geometry msc Generalized quadrangles and generalized polygons in finite geometry msc https://ems.press/doi/10.4171/110 cover image https://content.ems.press/assets/public/images/books/cover-112.png nam a22 5a 4500 10.4171/103 DE-4084 2012-06-08 a fot 00| 0| cr nn mmmmamaa 120608e20120608gw fot 00| 0|eng d 9783037196038 10.4171/103 doi DE-4084 PBKD bicssc 30-00 msc 32-00 msc 57-00 msc 32G13 msc 32G15 msc 30F60 msc 11F06 msc 11F75 msc 14D20 msc 14H15 msc 14H60 msc 14H55 msc 14J60 msc 20F14 msc 20F28 msc 20F38 msc 20F65 msc 20F67 msc 20H10 msc 30C62 msc 30F20 msc 30F25 msc 30F10 msc 30F15 msc 30F30 msc 30F35 msc 30F40 msc 30F45 msc 53A35 msc 53B35 msc 53C35 msc 53C50 msc 53C80 msc 53D55 msc 53Z05 msc 57M07 msc 57M50 msc 57M60 msc 57N16 msc Papadopoulos edt Handbook of Teichmüller Theory, Volume III. EMS Press 2012 1 online resource (874 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 17 2523-5141 Restricted to subscribers. https://ems.press/books The subject of this handbook is Teichmüller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with 3-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas towards a unique subject is a manifestation of the unity and harmony of mathematics. The present volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in the fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. * The metric and the analytic theory. * The group theory. * The algebraic topology of mapping class groups and moduli spaces. * Teichmüller theory and mathematical physics. The handbook is addressed to graduate students and researchers in all the fields mentioned. Complex analysis, complex variables bicssc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functions of a complex variable msc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to several complex variables and analytic spaces msc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to manifolds and cell complexes msc Complex-analytic moduli problems msc Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) msc Teichmüller theory for Riemann surfaces msc Structure of modular groups and generalizations; arithmetic groups msc Cohomology of arithmetic groups msc Algebraic moduli problems, moduli of vector bundles msc Families, moduli of curves (analytic) msc Vector bundles on curves and their moduli msc Riemann surfaces; Weierstrass points; gap sequences msc Vector bundles on surfaces and higher-dimensional varieties, and their moduli msc Derived series, central series, and generalizations for groups msc Automorphism groups of groups msc Other groups related to topology or analysis msc Geometric group theory msc Hyperbolic groups and nonpositively curved groups msc Fuchsian groups and their generalizations (group-theoretic aspects) msc Quasiconformal mappings in the complex plane msc Classification theory of Riemann surfaces msc Ideal boundary theory for Riemann surfaces msc Compact Riemann surfaces and uniformization msc Harmonic functions on Riemann surfaces msc Differentials on Riemann surfaces msc Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) msc Kleinian groups (aspects of compact Riemann surfaces and uniformization) msc Conformal metrics (hyperbolic, Poincaré, distance functions) msc Non-Euclidean differential geometry msc Local differential geometry of Hermitian and Kählerian structures msc Differential geometry of symmetric spaces msc Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics msc Applications of global differential geometry to the sciences msc Deformation quantization, star products msc Applications of differential geometry to physics msc Topological methods in group theory msc General geometric structures on low-dimensional manifolds msc Group actions on manifolds and cell complexes in low dimensions msc Geometric structures on manifolds of high or arbitrary dimension msc https://ems.press/doi/10.4171/103 cover image https://content.ems.press/assets/public/images/books/cover-113.jpg nam a22 5a 4500 10.4171/114 DE-4084 2012-08-15 a fot 00| 0| cr nn mmmmamaa 120815e20120815gw fot 00| 0|eng d 9783037196144 10.4171/114 doi DE-4084 PBMW bicssc 11S15 msc 13D10 msc 14-02 msc 14B05 msc 14B12 msc 14C17 msc 14C20 msc 14C35 msc 14D06 msc 14D15 msc 14D20 msc 14D23 msc 14E15 msc 14E30 msc 14F43 msc 14H10 msc 14H40 msc 14H42 msc 14J17 msc 14J28 msc 14J30 msc 14J32 msc 14J50 msc 14J70 msc 14K10 msc 14K25 msc 14L30 msc 14M15 msc 14M17 msc 14M25 msc 14N10 msc 14N15 msc 32G10 msc 32Q45 msc 34A30 msc 53D05 msc 55N91 msc 01-02 msc 01A70 msc 05E05 msc 11S85 msc 13A35 msc 14C30 msc 14F18 msc 14J26 msc 14N20 msc 19D55 msc 32S25 msc 53D20 msc 57R45 msc Pragacz edt Contributions to Algebraic Geometry ; Impanga Lecture Notes. EMS Press 2012 1 online resource (516 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 6 2523-5168 Restricted to subscribers. https://ems.press/books The articles in this volume are the outcome of the Impanga Conference on Algebraic Geometry in 2010 at the Banach Center in Będlewo. The following spectrum of topics is covered: * K3 surfaces and Enriques surfaces; * Prym varieties and their moduli; * invariants of singularities in birational geometry; * differential forms on singular spaces; * Minimal Model Program; * linear systems; * toric varieties; * Seshadri and packing constants; * equivariant cohomology; * Thom polynomials; * arithmetic questions. The main purpose of the volume is to give comprehensive introductions to the above topics through texts starting from an elementary level and ending with the discussion of current research. The first four topics are represented by the notes from the minicourses held during the conference. In the articles the reader will find classical results and methods, as well as modern ones. The book is addressed to researchers and graduate students in algebraic geometry, singularity theory and algebraic topology. Most of the material exposed in the volume has not yet appeared in book form. Algebraic geometry bicssc Ramification and extension theory msc Deformations and infinitesimal methods in commutative ring theory msc Research exposition (monographs, survey articles) pertaining to algebraic geometry msc Singularities in algebraic geometry msc Local deformation theory, Artin approximation, etc. msc Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry msc Divisors, linear systems, invertible sheaves msc Applications of methods of algebraic \(K\)-theory in algebraic geometry msc Fibrations, degenerations in algebraic geometry msc Formal methods and deformations in algebraic geometry msc Algebraic moduli problems, moduli of vector bundles msc Stacks and moduli problems msc Global theory and resolution of singularities (algebro-geometric aspects) msc Minimal model program (Mori theory, extremal rays) msc Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) msc Families, moduli of curves (algebraic) msc Jacobians, Prym varieties msc Theta functions and curves; Schottky problem msc Singularities of surfaces or higher-dimensional varieties msc \(K3\) surfaces and Enriques surfaces msc \(3\)-folds msc Calabi-Yau manifolds (algebro-geometric aspects) msc Automorphisms of surfaces and higher-dimensional varieties msc Hypersurfaces and algebraic geometry msc Algebraic moduli of abelian varieties, classification msc Theta functions and abelian varieties msc Group actions on varieties or schemes (quotients) msc Grassmannians, Schubert varieties, flag manifolds msc Homogeneous spaces and generalizations msc Toric varieties, Newton polyhedra, Okounkov bodies msc Enumerative problems (combinatorial problems) in algebraic geometry msc Classical problems, Schubert calculus msc Deformations of submanifolds and subspaces msc Hyperbolic and Kobayashi hyperbolic manifolds msc Linear ordinary differential equations and systems msc Symplectic manifolds (general theory) msc Equivariant homology and cohomology in algebraic topology msc Research exposition (monographs, survey articles) pertaining to history and biography msc Biographies, obituaries, personalia, bibliographies msc Symmetric functions and generalizations msc Other nonanalytic theory msc Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure msc Transcendental methods, Hodge theory (algebro-geometric aspects) msc Multiplier ideals msc Rational and ruled surfaces msc Configurations and arrangements of linear subspaces msc \(K\)-theory and homology; cyclic homology and cohomology msc Complex surface and hypersurface singularities msc Momentum maps; symplectic reduction msc Singularities of differentiable mappings in differential topology msc https://ems.press/doi/10.4171/114 cover image https://content.ems.press/assets/public/images/books/cover-117.jpg nam a22 5a 4500 10.4171/119 DE-4084 2012-10-19 a fot 00| 0| cr nn mmmmamaa 121019e20121019gw fot 00| 0|eng d 9783037196199 10.4171/119 doi DE-4084 PBMS bicssc 14-XX msc 11-XX msc de Jong edt Geometry and Arithmetic. EMS Press 2012 1 online resource (383 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 7 2523-5168 Restricted to subscribers. https://ems.press/books This volume contains 21 articles written by leading experts in the fields of algebraic and arithmetic geometry. The treated topics range over a variety of themes, including moduli spaces of curves and abelian varieties, algebraic cycles, vector bundles and coherent sheaves, curves over finite fields, and algebraic surfaces, among others. The volume originates from the conference Geometry and Arithmetic, which was held on the island of Schiermonnikoog in The Netherlands in September 2010. Analytic geometry bicssc Algebraic geometry msc Number theory msc Faber edt Farkas edt https://ems.press/doi/10.4171/119 cover image https://content.ems.press/assets/public/images/books/cover-115.jpg nam a22 5a 4500 10.4171/112 DE-4084 2012-10-10 a fot 00| 0| cr nn mmmmamaa 121010e20121010gw fot 00| 0|eng d 9783037196120 10.4171/112 doi DE-4084 PBM bicssc 51-01 msc 20F69 msc 19K56 msc 57-01 msc 46L87 msc 58B34 msc 46L99 msc 53C20 msc Nowak aut Large Scale Geometry. EMS Press 2012 1 online resource (203 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 12 2943-4955 Restricted to subscribers. https://ems.press/books Large scale geometry is the study of geometric objects viewed from a great distance. The idea of large scale geometry can be traced back to Mostows work on rigidity and the work of Švarc, Milnor and Wolf on growth of groups. In the last decades, large scale geometry has found important applications in group theory, topology, geometry, higher index theory, computer science, and large data analysis. This book provides a friendly approach to the basic theory of this exciting and fast growing subject and offers a glimpse of its applications to topology, geometry, and higher index theory. The authors have made a conscientious effort to make the book accessible to advanced undergraduate students, graduate students, and non-experts. This book has appeared in a [second edition](https://doi.org/10.4171/etb/26) in 2023. Geometry bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry msc Asymptotic properties of groups msc Index theory msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes msc Noncommutative differential geometry msc Noncommutative geometry (à la Connes) msc Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.) msc Global Riemannian geometry, including pinching msc Yu aut https://ems.press/doi/10.4171/112 cover image https://content.ems.press/assets/public/images/books/cover-114.jpg nam a22 5a 4500 10.4171/116 DE-4084 2012-10-29 a fot 00| 0| cr nn mmmmamaa 121029e20121029gw fot 00| 0|eng d 9783037196168 10.4171/116 doi DE-4084 PB bicssc 65-02 msc 65Y20 msc 68Q17 msc 68Q25 msc 41A63 msc 46E22 msc 28C20 msc 46E30 msc 65N99 msc 65R20 msc Novak aut Tractability of Multivariate Problems. Volume III. Standard Information for Operators EMS Press 2012 1 online resource (604 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 18 2943-5005 Restricted to subscribers. https://ems.press/books This three-volume set is a comprehensive study of the tractability of multivariate problems. Volume I covers algorithms using linear information consisting of arbitrary continuous linear functionals. Volumes II and III are devoted to algorithms using standard information consisting of function values. Approximation of linear and selected nonlinear _functionals_ is dealt with in volume II, and linear and selected nonlinear _operators_ are studied in volume III. To a large extent, volume III can be read independently of volumes I and II. The most important example studied in volume III is the approximation of multivariate functions. It turns out that many other linear and some nonlinear problems are closely related to the approximation of multivariate functions. While the lower bounds obtained in volume I for the class of linear information also yield lower bounds for the standard class of function values, new techniques for upper bounds are presented in volume III. One of the main issues here is to verify when the power of standard information is nearly the same as the power of linear information. In particular, for the approximation problem defined over Hilbert spaces, the power of standard and linear information is the same in the randomized and average case (with Gaussian measures) settings, whereas in the worst case setting this is not true. The book is of interest to researchers working in computational mathematics, especially in approximation of high-dimensiona problems. It may be well suited for graduate courses and seminars. The text contains 58 open problems for future research in tractability. Mathematics bicssc Research exposition (monographs, survey articles) pertaining to numerical analysis msc Complexity and performance of numerical algorithms msc Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) msc Analysis of algorithms and problem complexity msc Multidimensional problems msc Hilbert spaces with reproducing kernels ( (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) msc Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) msc Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) msc Numerical methods for partial differential equations, boundary value problems msc Numerical methods for integral equations msc Woźniakowski aut https://ems.press/doi/10.4171/116 cover image https://content.ems.press/assets/public/images/books/cover-116.jpg nam a22 5a 4500 10.4171/118 DE-4084 2012-12-18 a fot 00| 0| cr nn mmmmamaa 121218e20121218gw fot 00| 0|eng d 9783037196182 10.4171/118 doi DE-4084 PBMW bicssc 13A35 msc 14A22 msc 14B05 msc 14B07 msc 14B15 msc 14C17 msc 14D06 msc 14E15 msc 14E18 msc 14F99 msc 14H25 msc 14J17 msc 14M25 msc 14N99 msc 18F30 msc 32A27 msc 32C37 msc 32G15 msc 35Q75 msc 52C35 msc 53C05 msc 55N35 msc 55R40 msc 57R18 msc 57R20 msc 58A30 msc 58K10 msc 58K40 msc 58K60 msc 60D05 msc 83C57 msc Blanlil edt Singularities in Geometry and Topology ; Strasbourg 2009. EMS Press 2012 1 online resource (370 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 20 2523-5141 Restricted to subscribers. https://ems.press/books This volume arises from 5th Franco-Japanese Symposium on Singularities, held in Strasbourg in August 2009. The conference brought together an international group of researchers working on singularities in algebraic geometry, analytic geometry and topology, mainly from France and Japan. Besides, it also organized a special session, JSPS Forum on Singularities and Applications, which was aimed to introduce some recent applications of singularity theory to physics and statistics. This book comprises research papers and short lecture notes on advanced topics on singularities. Some surveys on applications that were presented in the Forum are also added. Topics covered include splice surface singularities, b\-functions, equisingularity, degenerating families of Riemann surfaces, hyperplane arrangements, mixed singularities, jet schemes, noncommutative blow-ups, characteristic classes of singular spaces, and applications to geometric optics, cosmology and learning theory. Graduate students who wish to learn about various approaches to singularities, as well as experts in the field and researchers in other areas of mathematics and science will find the contributions to this volume a rich source for further study and research. Algebraic geometry bicssc Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure msc Noncommutative algebraic geometry msc Singularities in algebraic geometry msc Deformations of singularities msc Local cohomology and algebraic geometry msc Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry msc Fibrations, degenerations in algebraic geometry msc Global theory and resolution of singularities (algebro-geometric aspects) msc Arcs and motivic integration msc (Co)homology theory in algebraic geometry msc Arithmetic ground fields for curves msc Singularities of surfaces or higher-dimensional varieties msc Toric varieties, Newton polyhedra, Okounkov bodies msc Projective and enumerative algebraic geometry msc Grothendieck groups (category-theoretic aspects) msc Residues for several complex variables msc Duality theorems for analytic spaces msc Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) msc PDEs in connection with relativity and gravitational theory msc Arrangements of points, flats, hyperplanes (aspects of discrete geometry) msc Connections (general theory) msc Other homology theories in algebraic topology msc Homology of classifying spaces and characteristic classes in algebraic topology msc Topology and geometry of orbifolds msc Characteristic classes and numbers in differential topology msc Vector distributions (subbundles of the tangent bundles) msc Monodromy on manifolds msc Classification; finite determinacy of map germs msc Deformation of singularities msc Geometric probability and stochastic geometry msc Black holes msc Ohmoto edt https://ems.press/doi/10.4171/118 cover image https://content.ems.press/assets/public/images/books/cover-118.jpg nam a22 5a 4500 10.4171/115 DE-4084 2013-01-07 a fot 00| 0| cr nn mmmmamaa 130107e20130107gw fot 00| 0|eng d 9783037196151 10.4171/115 doi DE-4084 PBMW bicssc 13D09 msc 14-02 msc 14-06 msc 16E35 msc 13D02 msc 13D10 msc 14A22 msc 14E08 msc 14E16 msc 14E30 msc 14J32 msc 14J33 msc 14J45 msc 14K05 msc 14L24 msc 14N35 msc 16E05 msc 16E40 msc 18G10 msc 20G05 msc 20G15 msc Kawamata edt Derived Categories in Algebraic Geometry ; Tokyo 2011. EMS Press 2013 1 online resource (354 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 8 2523-5168 Restricted to subscribers. https://ems.press/books The study of derived categories is a subject that attracts increasingly many young mathematicians from various fields of mathematics, including abstract algebra, algebraic geometry, representation theory and mathematical physics. The concept of the derived category of sheaves was invented by Grothendieck and Verdier in the 1960s as a tool to express important results in algebraic geometry such as the duality theorem. In the 1970s, Beilinson, Gelfand and Gelfand discovered that a derived category of an algebraic variety may be equivalent to that of a finite dimensional non-commutative algebra, and Mukai found that there are non-isomorphic algebraic varieties that have equivalent derived categories. In this way the derived category provides a new concept that has many incarnations. In the 1990s, Bondal and Orlov uncovered an unexpected parallelism between derived categories and birational geometry. Kontsevichs homological mirror symmetry provided further motivation for the study of derived categories. This book is the proceedings of a conference held at the University of Tokyo in January 2011 on the current status of the research on derived categories related to algebraic geometry. Most articles are survey papers on this rapidly developing field. The book is suitable for young mathematicians who want to enter this exciting field. Some basic knowledge of algebraic geometry is assumed. Algebraic geometry bicssc Derived categories and commutative rings msc Research exposition (monographs, survey articles) pertaining to algebraic geometry msc Proceedings, conferences, collections, etc. pertaining to algebraic geometry msc Derived categories and associative algebras msc Syzygies, resolutions, complexes and commutative rings msc Deformations and infinitesimal methods in commutative ring theory msc Noncommutative algebraic geometry msc Rationality questions in algebraic geometry msc McKay correspondence msc Minimal model program (Mori theory, extremal rays) msc Calabi-Yau manifolds (algebro-geometric aspects) msc Mirror symmetry (algebro-geometric aspects) msc Fano varieties msc Algebraic theory of abelian varieties msc Geometric invariant theory msc Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) msc Syzygies, resolutions, complexes in associative algebras msc (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) msc Resolutions; derived functors (category-theoretic aspects) msc Representation theory for linear algebraic groups msc Linear algebraic groups over arbitrary fields msc https://ems.press/doi/10.4171/115 cover image https://content.ems.press/assets/public/images/books/cover-119.jpg nam a22 5a 4500 10.4171/113 DE-4084 2013-01-24 a fot 00| 0| cr nn mmmmamaa 130124e20130124gw fot 00| 0|eng d 9783037196137 10.4171/113 doi DE-4084 PBX bicssc 01-02 msc 03-03 msc 11-03 msc 12-03 msc 16-03 msc 20-03 msc 01A60 msc 01A70 msc 01A75 msc 11E04 msc 11E88 msc 11R18 msc 11R37 msc 11U10 msc Roquette aut Contributions to the History of Number Theory in the 20th Century. EMS Press 2013 1 online resource (289 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 7 2523-5222 Restricted to subscribers. https://ems.press/books The 20th century was a time of great upheaval and great progress, mathematics not excluded. In order to get the overall picture of trends, developments and results it is illuminating to look at their manifestations locally, in the personal life and work of people living at the time. The university archives of Göttingen harbor a wealth of papers, letters and manuscripts from several generations of mathematicians - documents which tell us the story of the historic developments from a local point of view. The present book offers a number of essays based on documents from Göttingen and elsewhere - essays which are not yet contained in the authors Collected Works. These little pieces, independent from each other, are meant as contributions to the imposing mosaic of history of number theory. They are written for mathematicians but with no special background requirements. Involved are the names of Abraham Adrian Albert, Cahit Arf, Emil Artin, Richard Brauer, Otto Grün, Helmut Hasse, Klaus Hoechsmann, Robert Langlands, Heinrich-Wolfgang Leopoldt, Emmy Noether, Abraham Robinson, Ernst Steinitz, Hermann Weyl and others. History of mathematics bicssc Research exposition (monographs, survey articles) pertaining to history and biography msc History of mathematical logic and foundations msc History of number theory msc History of field theory msc History of associative rings and algebras msc History of group theory msc History of mathematics in the 20th century msc Biographies, obituaries, personalia, bibliographies msc Collected or selected works; reprintings or translations of classics msc Quadratic forms over general fields msc Quadratic spaces; Clifford algebras msc Cyclotomic extensions msc Class field theory msc Nonstandard arithmetic (number-theoretic aspects) msc https://ems.press/doi/10.4171/113 cover image https://content.ems.press/assets/public/images/books/cover-120.jpg nam a22 5a 4500 10.4171/121 DE-4084 2013-04-11 a fot 00| 0| cr nn mmmmamaa 130411e20130411gw fot 00| 0|eng d 9783037196212 10.4171/121 doi DE-4084 PBX bicssc 01-02 msc 81-02 msc 81-03 msc 81P05 msc 81P15 msc Reiter edt Erwin Schrödinger - 50 Years After. EMS Press 2013 1 online resource (195 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda ESI Lectures in Mathematics and Physics (esi) 9 2943-4939 Restricted to subscribers. https://ems.press/books Erwin Schrödinger (1887-1961) was an Austrian physicist famous for the equation named after him and which earned him the Nobel Prize in 1933. This book contains lectures presented at the international symposium _Erwin Schrödinger - 50 Years After_ held at the Erwin Schrödinger International Institute for Mathematical Physics in January 2011 to commemorate the 50th anniversary of Schrödingers death. The text covers a broad spectrum of topics ranging from personal reminiscences to foundational questions of quantum mechanics and historical accounts of Schrödingers work. Besides the lectures presented at the symposium the volume also contains articles specially written for this occasion. The contributions give an overview of Schrödingers legacy to the sciences from the standpoint of some of present days leading scholars in the field. The book addresses students and researchers in mathematics, physics and the history of science. History of mathematics bicssc Research exposition (monographs, survey articles) pertaining to history and biography msc Research exposition (monographs, survey articles) pertaining to quantum theory msc History of quantum theory msc General and philosophical questions in quantum theory msc Quantum measurement theory, state operations, state preparations msc Yngvason edt https://ems.press/doi/10.4171/121 cover image https://content.ems.press/assets/public/images/books/cover-121.jpg nam a22 5a 4500 10.4171/111 DE-4084 2013-05-06 a fot 00| 0| cr nn mmmmamaa 130506e20130506gw fot 00| 0|eng d 9783037196113 10.4171/111 doi DE-4084 PBKD bicssc 30-01 msc 31-01 msc Bruna aut Complex Analysis ; Translated from the Catalan by Ignacio Monreal. EMS Press 2013 1 online resource (576 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 13 2943-4955 Restricted to subscribers. https://ems.press/books The theory of functions of a complex variable is a central theme in mathematical analysis that has links to several branches of mathematics. Understanding the basics of the theory is necessary for anyone who wants to have a general mathematical training or for anyone who wants to use mathematics in applied sciences or technology. The book presents the basic theory of analytic functions of a complex variable and their points of contact with other parts of mathematical analysis. This results in some new approaches to a number of topics when compared to the current literature on the subject. Some issues covered are: a real version of the Cauchy-Goursat theorem, theorems of vector analysis with weak regularity assumptions, an approach to the concept of holomorphic functions of real variables, Greens formula with multiplicities, Cauchys theorem for locally exact forms, a study in parallel of Poissons equation and the inhomogeneous Cauchy-Riemann equations, the relationship between Greens function and conformal mapping, the connection between the solution of Poissons equation and zeros of holomorphic functions, and the Whittaker-Shannon theorem of information theory. The text can be used as a manual for complex variable courses of various levels and as a reference book. The only prerequisites for reading it is a working knowledge of the topology of the plane and the differential calculus for functions of several real variables. A detailed treatment of harmonic functions also makes the book useful as an introduction to potential theory. Complex analysis, complex variables bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to potential theory msc Cufí aut https://ems.press/doi/10.4171/111 cover image https://content.ems.press/assets/public/images/books/cover-122.jpg nam a22 5a 4500 10.4171/122 DE-4084 2013-05-29 a fot 00| 0| cr nn mmmmamaa 130529e20130529gw fot 00| 0|eng d 9783037196229 10.4171/122 doi DE-4084 PBK bicssc 30C65 msc 30C75 msc 35J46 msc 35J50 msc 35J56 msc 35J70 msc 35Q35 msc 35Q60 msc 37F40 msc 57R99 msc Bojarski aut Infinitesimal Geometry of Quasiconformal and Bi-Lipschitz Mappings in the Plane. EMS Press 2013 1 online resource (214 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 19 2943-5005 Restricted to subscribers. https://ems.press/books This book is intended for researchers interested in new aspects of local behavior of plane mappings and their applications. The presentation is self-contained, but the reader is assumed to know basic complex and real analysis. The study of the local and boundary behavior of quasiconformal and bi-Lipschitz mappings in the plane forms the core of the book. The concept of the infinitesimal space is used to investigate the behavior of a mapping at points without differentiability. This concept, based on compactness properties, is applied to regularity problems of quasiconformal mappings and quasiconformal curves, boundary behavior, weak and asymptotic conformality, local winding properties, variation of quasiconformal mappings, and criteria of univalence. Quasiconformal and bi-Lipschitz mappings are instrumental for understanding elasticity, control theory and tomography and the book also offers a new look at the classical areas such as the boundary regularity of a conformal map. Complicated local behavior is illustrated by many examples. The text offers a detailed development of the background for graduate students and researchers. Starting with the classical methods to study quasiconformal mappings, this treatment advances to the concept of the infinitesimal space and then relates it to other regularity properties of mappings in Part II. The new unexpected connections between quasiconformal and bi-Lipschitz mappings are treated in Part III. There is an extensive bibliography. Calculus & mathematical analysis bicssc Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations msc Extremal problems for conformal and quasiconformal mappings, other methods msc First-order elliptic systems msc Variational methods for elliptic systems msc Boundary value problems for first-order elliptic systems msc Degenerate elliptic equations msc PDEs in connection with fluid mechanics msc PDEs in connection with optics and electromagnetic theory msc Geometric limits in holomorphic dynamics msc Differential topology msc Gutlyanskii aut Martio aut Ryazanov aut https://ems.press/doi/10.4171/122 cover image https://content.ems.press/assets/public/images/books/cover-125.jpg nam a22 5a 4500 10.4171/123 DE-4084 2013-05-29 a fot 00| 0| cr nn mmmmamaa 130529e20130529gw fot 00| 0|eng d 9783037196236 10.4171/123 doi DE-4084 PB bicssc 46-02 msc 46E35 msc 42B35 msc 42C40 msc 35K05 msc 35Q30 msc 76D03 msc 76D05 msc Triebel aut Local Function Spaces, Heat and Navier-Stokes Equations. EMS Press 2013 1 online resource (241 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 20 2943-5005 Restricted to subscribers. https://ems.press/books In this book a new approach is presented to exhibit relations between Sobolev spaces, Besov spaces, and Hölder-Zygmund spaces on the one hand and Morrey-Campanato spaces on the other. Morrey-Campanato spaces extend the notion of functions of bounded mean oscillation. These spaces play an important role in the theory of linear and nonlinear PDEs. Chapters 1-3 deal with local smoothness spaces in Euclidean n\-space based on the Morrey-Campanato refinement of the Lebesgue spaces. The presented approach relies on wavelet decompositions. This is applied in Chapter 4 to Gagliardo-Nirenberg inequalities. Chapter 5 deals with linear and nonlinear heat equations in global and local function spaces. The obtained assertions about function spaces and nonlinear heat equations are used in Chapter 6 to study Navier-Stokes equations. The book is addressed to graduate students and mathematicians having a working knowledge of basic elements of (global) function spaces, and who are interested in applications to nonlinear PDEs with heat and Navier-Stokes equations as prototypes. Mathematics bicssc Research exposition (monographs, survey articles) pertaining to functional analysis msc Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems msc Function spaces arising in harmonic analysis msc Nontrigonometric harmonic analysis involving wavelets and other special systems msc Heat equation msc Navier-Stokes equations msc Existence, uniqueness, and regularity theory for incompressible viscous fluids msc Navier-Stokes equations for incompressible viscous fluids msc https://ems.press/doi/10.4171/123 cover image https://content.ems.press/assets/public/images/books/cover-226.jpg nam a22 5a 4500 10.4171/124 DE-4084 2013-08-07 a fot 00| 0| cr nn mmmmamaa 130807e20130807gw fot 00| 0|eng d 9783037196243 10.4171/124 doi DE-4084 PBK bicssc 37-02 msc 37Cxx msc 37Dxx msc 34Cxx msc 34Dxx msc 65Lxx msc 65P10 msc Nipp aut Invariant Manifolds in Discrete and Continuous Dynamical Systems. EMS Press 2013 1 online resource (225 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 21 2943-5005 Restricted to subscribers. https://ems.press/books In this book dynamical systems are investigated from a geometric viewpoint. Admitting an invariant manifold is a strong geometric property of a dynamical system. This text presents rigorous results on invariant manifolds and gives examples of possible applications. In the first part discrete dynamical systems in Banach spaces are considered. Results on the existence and smoothness of attractive and repulsive invariant manifolds are derived. In addition, perturbations and approximations of the manifolds and the foliation of the adjacent space are treated. In the second part analogous results for continuous dynamical systems in finite dimensions are established. In the third part the theory developed is applied to problems in numerical analysis and to singularly perturbed systems of ordinary differential equations. The mathematical approach is based on the so-called graph transform, already used by Hadamard in 1901. The aim is to establish invariant manifold results in a simple setting providing quantitative estimates. The book is targeted at researchers in the field of dynamical systems interested in precise theorems easy to apply. The application part might also serve as an underlying text for a student seminar in mathematics. Calculus & mathematical analysis bicssc Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory msc Smooth dynamical systems: general theory msc Dynamical systems with hyperbolic behavior msc Qualitative theory for ordinary differential equations msc Stability theory for ordinary differential equations msc Numerical methods for ordinary differential equations msc Numerical methods for Hamiltonian systems including symplectic integrators msc Stoffer aut https://ems.press/doi/10.4171/124 cover image https://content.ems.press/assets/public/images/books/cover-123.jpg nam a22 5a 4500 10.4171/126 DE-4084 2013-11-15 a fot 00| 0| cr nn mmmmamaa 131115e20131115gw fot 00| 0|eng d 9783037196267 10.4171/126 doi DE-4084 PB bicssc 00B60 msc 05-XX msc 17-XX msc 20-XX msc 22-XX msc 51-XX msc Buekenhout edt Jacques Tits, uvres - Collected Works. EMS Press 2013 1 online resource (3963 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 8 2523-5222 Restricted to subscribers. https://ems.press/books Jacques Tits was awarded the Wolf Prize in 1993 and the Abel Prize (jointly with John Thompson) in 2008. The impact of his contributions in algebra, group theory and geometry made over a span of more than five decades is incalculable. Many fundamental developments in several fields of mathematics have their origin in ideas of Tits. A number of Tits papers mark the starting point of completely new directions of research. Outstanding examples are papers on quadratic forms, on Kac-Moody groups and on what subsequently became known as the Tits-alternative. These volumes contain an almost complete collection of Tits mathematical writings. They include, in particular, a number of published and unpublished manuscripts which have not been easily accessible until now. This collection of Tits contributions in one place makes the evolution of his mathematical thinking visible. The development of his theory of buildings and _BN_\-pairs and its bearing on the theory of algebraic groups, for example, reveal a fascinating story. Along with Tits mathematical writings, these volumes contain biographical data, survey articles on aspects of Tits work and comments by the editors on the content of some of his papers. With the publication of these volumes, a major piece of 20th century mathematics is being made available to a wider audience. Mathematics bicssc Collections of reprinted articles msc Combinatorics msc Nonassociative rings and algebras msc Group theory and generalizations msc Topological groups, Lie groups msc Geometry msc Mühlherr edt Tignol edt van Maldeghem edt https://ems.press/doi/10.4171/126 cover image https://content.ems.press/assets/public/images/books/cover-124.jpg nam a22 5a 4500 10.4171/126-1 DE-4084 2013-11-15 a fot 00| 0| cr nn mmmmamaa 131115e20131115gw fot 00| 0|eng d 9783985475308 10.4171/126-1 doi DE-4084 PB bicssc 00B60 msc 05-XX msc 17-XX msc 20-XX msc 22-XX msc 51-XX msc Buekenhout edt Jacques Tits, uvres - Collected Works. Volume I EMS Press 2013 1 online resource (3963 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 8 2523-5222 Restricted to subscribers. https://ems.press/books Jacques Tits was awarded the Wolf Prize in 1993 and the Abel Prize (jointly with John Thompson) in 2008. The impact of his contributions in algebra, group theory and geometry made over a span of more than five decades is incalculable. Many fundamental developments in several fields of mathematics have their origin in ideas of Tits. A number of Tits papers mark the starting point of completely new directions of research. Outstanding examples are papers on quadratic forms, on Kac-Moody groups and on what subsequently became known as the Tits-alternative. These volumes contain an almost complete collection of Tits mathematical writings. They include, in particular, a number of published and unpublished manuscripts which have not been easily accessible until now. This collection of Tits contributions in one place makes the evolution of his mathematical thinking visible. The development of his theory of buildings and _BN_\-pairs and its bearing on the theory of algebraic groups, for example, reveal a fascinating story. Along with Tits mathematical writings, these volumes contain biographical data, survey articles on aspects of Tits work and comments by the editors on the content of some of his papers. With the publication of these volumes, a major piece of 20th century mathematics is being made available to a wider audience. Mathematics bicssc Collections of reprinted articles msc Combinatorics msc Nonassociative rings and algebras msc Group theory and generalizations msc Topological groups, Lie groups msc Geometry msc Mühlherr edt Tignol edt van Maldeghem edt https://ems.press/doi/10.4171/126-1 cover image https://content.ems.press/assets/public/images/books/cover-227.jpg nam a22 5a 4500 10.4171/126-2 DE-4084 2013-11-15 a fot 00| 0| cr nn mmmmamaa 131115e20131115gw fot 00| 0|eng d 9783985475315 10.4171/126-2 doi DE-4084 PB bicssc 00B60 msc 05-XX msc 17-XX msc 20-XX msc 22-XX msc 51-XX msc Buekenhout edt Jacques Tits, uvres - Collected Works. Volume II EMS Press 2013 1 online resource (3963 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 8 2523-5222 Restricted to subscribers. https://ems.press/books Jacques Tits was awarded the Wolf Prize in 1993 and the Abel Prize (jointly with John Thompson) in 2008. The impact of his contributions in algebra, group theory and geometry made over a span of more than five decades is incalculable. Many fundamental developments in several fields of mathematics have their origin in ideas of Tits. A number of Tits papers mark the starting point of completely new directions of research. Outstanding examples are papers on quadratic forms, on Kac-Moody groups and on what subsequently became known as the Tits-alternative. These volumes contain an almost complete collection of Tits mathematical writings. They include, in particular, a number of published and unpublished manuscripts which have not been easily accessible until now. This collection of Tits contributions in one place makes the evolution of his mathematical thinking visible. The development of his theory of buildings and _BN_\-pairs and its bearing on the theory of algebraic groups, for example, reveal a fascinating story. Along with Tits mathematical writings, these volumes contain biographical data, survey articles on aspects of Tits work and comments by the editors on the content of some of his papers. With the publication of these volumes, a major piece of 20th century mathematics is being made available to a wider audience. Mathematics bicssc Collections of reprinted articles msc Combinatorics msc Nonassociative rings and algebras msc Group theory and generalizations msc Topological groups, Lie groups msc Geometry msc Mühlherr edt Tignol edt van Maldeghem edt https://ems.press/doi/10.4171/126-2 cover image https://content.ems.press/assets/public/images/books/cover-228.jpg nam a22 5a 4500 10.4171/126-3 DE-4084 2013-11-15 a fot 00| 0| cr nn mmmmamaa 131115e20131115gw fot 00| 0|eng d 9783985475322 10.4171/126-3 doi DE-4084 PB bicssc 00B60 msc 05-XX msc 17-XX msc 20-XX msc 22-XX msc 51-XX msc Buekenhout edt Jacques Tits, uvres - Collected Works. Volume III EMS Press 2013 1 online resource (3963 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 8 2523-5222 Restricted to subscribers. https://ems.press/books Jacques Tits was awarded the Wolf Prize in 1993 and the Abel Prize (jointly with John Thompson) in 2008. The impact of his contributions in algebra, group theory and geometry made over a span of more than five decades is incalculable. Many fundamental developments in several fields of mathematics have their origin in ideas of Tits. A number of Tits papers mark the starting point of completely new directions of research. Outstanding examples are papers on quadratic forms, on Kac-Moody groups and on what subsequently became known as the Tits-alternative. These volumes contain an almost complete collection of Tits mathematical writings. They include, in particular, a number of published and unpublished manuscripts which have not been easily accessible until now. This collection of Tits contributions in one place makes the evolution of his mathematical thinking visible. The development of his theory of buildings and _BN_\-pairs and its bearing on the theory of algebraic groups, for example, reveal a fascinating story. Along with Tits mathematical writings, these volumes contain biographical data, survey articles on aspects of Tits work and comments by the editors on the content of some of his papers. With the publication of these volumes, a major piece of 20th century mathematics is being made available to a wider audience. Mathematics bicssc Collections of reprinted articles msc Combinatorics msc Nonassociative rings and algebras msc Group theory and generalizations msc Topological groups, Lie groups msc Geometry msc Mühlherr edt Tignol edt van Maldeghem edt https://ems.press/doi/10.4171/126-3 cover image https://content.ems.press/assets/public/images/books/cover-126.jpg nam a22 5a 4500 10.4171/126-4 DE-4084 2013-11-15 a fot 00| 0| cr nn mmmmamaa 131115e20131115gw fot 00| 0|eng d 9783985475339 10.4171/126-4 doi DE-4084 PB bicssc 00B60 msc 05-XX msc 17-XX msc 20-XX msc 22-XX msc 51-XX msc Buekenhout edt Jacques Tits, uvres - Collected Works. Volume IV EMS Press 2013 1 online resource (3963 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 8 2523-5222 Restricted to subscribers. https://ems.press/books Jacques Tits was awarded the Wolf Prize in 1993 and the Abel Prize (jointly with John Thompson) in 2008. The impact of his contributions in algebra, group theory and geometry made over a span of more than five decades is incalculable. Many fundamental developments in several fields of mathematics have their origin in ideas of Tits. A number of Tits papers mark the starting point of completely new directions of research. Outstanding examples are papers on quadratic forms, on Kac-Moody groups and on what subsequently became known as the Tits-alternative. These volumes contain an almost complete collection of Tits mathematical writings. They include, in particular, a number of published and unpublished manuscripts which have not been easily accessible until now. This collection of Tits contributions in one place makes the evolution of his mathematical thinking visible. The development of his theory of buildings and _BN_\-pairs and its bearing on the theory of algebraic groups, for example, reveal a fascinating story. Along with Tits mathematical writings, these volumes contain biographical data, survey articles on aspects of Tits work and comments by the editors on the content of some of his papers. With the publication of these volumes, a major piece of 20th century mathematics is being made available to a wider audience. Mathematics bicssc Collections of reprinted articles msc Combinatorics msc Nonassociative rings and algebras msc Group theory and generalizations msc Topological groups, Lie groups msc Geometry msc Mühlherr edt Tignol edt van Maldeghem edt https://ems.press/doi/10.4171/126-4 cover image https://content.ems.press/assets/public/images/books/cover-198.jpg nam a22 5a 4500 10.4171/127 DE-4084 2013-12-13 a fot 00| 0| cr nn mmmmamaa 131213e20131213gw fot 00| 0|eng d 9783037196274 10.4171/127 doi DE-4084 PBMP bicssc 53D30 msc 53C10 msc 58D27 msc 32G15 msc 58J28 msc Labourie aut Lectures on Representations of Surface Groups. EMS Press 2013 1 online resource (145 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 17 2943-4971 Restricted to subscribers. https://ems.press/books The subject of these notes is the character variety of representations of a surface group in a Lie group. We emphasize the various points of view (combinatorial, differential, algebraic) and are interested in the description of its smooth points, symplectic structure, volume and connected components. We also show how a three manifold bounded by the surface leaves a trace in this character variety. These notes were originally designed for students with only elementary knowledge of differential geometry and topology. In the first chapters, we do not insist in the details of the differential geometric constructions and refer to classical textbooks, while in the more advanced chapters proofs occasionally are provided only for special cases where they convey the flavor of the general arguments. These notes could also be used by researchers entering this fast expanding field as motivation for further studies proposed in a concluding paragraph of every chapter. Differential & Riemannian geometry bicssc Symplectic structures of moduli spaces msc \(G\)-structures msc Moduli problems for differential geometric structures msc Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) msc Eta-invariants, Chern-Simons invariants msc https://ems.press/doi/10.4171/127 cover image https://content.ems.press/assets/public/images/books/cover-203.jpg nam a22 5a 4500 10.4171/120 DE-4084 2014-01-03 a fot 10| 0| cr nn mmmmamaa 140103e20140103gw fot 10| 0|eng d 9783037196205 10.4171/120 doi DE-4084 P bicssc PB bicssc 00Bxx msc Latała edt European Congress of Mathematics ; Kraków, 2 - 7 July, 2012. EMS Press 2014 1 online resource (824 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books The European Congress of Mathematics, held every four years, has become a well-established major international mathematical event. Following those in Paris (1992), Budapest (1996), Barcelona (2000), Stockholm (2004) and Amsterdam (2008), the Sixth European Congress of Mathematics (6ECM) took place in Kraków, Poland, July 2-7, 2012, with about 1000 participants from all over the world. Ten plenary, thirty-three invited lectures and three special lectures formed the core of the program. As at all the previous EMS congresses, ten outstanding young mathematicians received the EMS prizes in recognition of their research achievements. In addition, two more prizes were awarded: the Felix Klein Prize for a remarkable solution of an industrial problem, and - for the first time - the Otto Neugebauer Prize for a highly original and influential piece of work in the history of mathematics. The program was complemented by twenty-four minisymposia with nearly 100 talks, spread over all areas of mathematics. Six panel discussions were organized, covering a variety of issues ranging from the financing of mathematical research to gender imbalance in mathematics. These proceedings present extended versions of most of the invited talks which were delivered during the congress, providing a permanent record of the best what mathematics offers today. Mathematics & science bicssc Mathematics bicssc Conference proceedings and collections of articles msc Ruciński edt Strzelecki edt Świątkowski edt Wrzosek edt Zakrzewski edt https://ems.press/doi/10.4171/120 cover image https://content.ems.press/assets/public/images/books/cover-229.png nam a22 5a 4500 10.4171/130 DE-4084 2014-01-18 a fot 00| 0| cr nn mmmmamaa 140118e20140118gw fot 00| 0|eng d 9783037196304 10.4171/130 doi DE-4084 PB bicssc 13F60 msc 05E40 msc 14M15 msc 17B22 msc 17B63 msc 20F55 msc 51F15 msc 52B05 msc 52B11 msc 57Q15 msc Marsh aut Lecture Notes on Cluster Algebras. EMS Press 2014 1 online resource (121 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 19 2943-4971 Restricted to subscribers. https://ems.press/books Cluster algebras are combinatorially defined commutative algebras which were introduced by S. Fomin and A. Zelevinsky as a tool for studying the dual canonical basis of a quantized enveloping algebra and totally positive matrices. The aim of these notes is to give an introduction to cluster algebras which is accessible to graduate students or researchers interested in learning more about the field, while giving a taste of the wide connections between cluster algebras and other areas of mathematics. The approach taken emphasizes combinatorial and geometric aspects of cluster algebras. Cluster algebras of finite type are classified by the Dynkin diagrams, so a short introduction to reflection groups is given in order to describe this and the corresponding generalized associahedra. A discussion of cluster algebra periodicity, which has a close relationship with discrete integrable systems, is included. The book ends with a description of the cluster algebras of finite mutation type and the cluster structure of the homogeneous coordinate ring of the Grassmannian, both of which have a beautiful description in terms of combinatorial geometry. Mathematics bicssc Cluster algebras msc Combinatorial aspects of commutative algebra msc Grassmannians, Schubert varieties, flag manifolds msc Root systems msc Poisson algebras msc Reflection and Coxeter groups (group-theoretic aspects) msc Reflection groups, reflection geometries msc Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) msc \(n\)-dimensional polytopes msc Triangulating manifolds msc https://ems.press/doi/10.4171/130 cover image https://content.ems.press/assets/public/images/books/cover-201.jpg nam a22 5a 4500 10.4171/129 DE-4084 2014-01-18 a fot 00| 0| cr nn mmmmamaa 140118e20140118gw fot 00| 0|eng d 9783037196298 10.4171/129 doi DE-4084 PBKJ bicssc 35Q20 msc 35Q70 msc Gallagher aut From Newton to Boltzmann: Hard Spheres and Short-range Potentials. EMS Press 2014 1 online resource (148 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 18 2943-4971 Restricted to subscribers. https://ems.press/books The question addressed in this monograph is the relationship between the time-reversible Newton dynamics for a system of particles interacting via elastic collisions, and the irreversible Boltzmann dynamics which gives a statistical description of the collision mechanism. Two types of elastic collisions are considered: hard spheres, and compactly supported potentials.. Following the steps suggested by Lanford in 1974, we describe the transition from Newton to Boltzmann by proving a rigorous convergence result in short time, as the number of particles tends to infinity and their size simultaneously goes to zero, in the Boltzmann-Grad scaling. Boltzmanns kinetic theory rests on the assumption that particle independence is propagated by the dynamics. This assumption is central to the issue of appearance of irreversibility. For finite numbers of particles, correlations are generated by collisions. The convergence proof establishes that for initially independent configurations, independence is statistically recovered in the limit. This book is intended for mathematicians working in the fields of partial differential equations and mathematical physics, and is accessible to graduate students with a background in analysis. Differential calculus & equations bicssc Boltzmann equations msc PDEs in connection with mechanics of particles and systems of particles msc Saint-Raymond aut Texier aut https://ems.press/doi/10.4171/129 cover image https://content.ems.press/assets/public/images/books/cover-206.png nam a22 5a 4500 10.4171/125 DE-4084 2014-01-03 a fot 00| 0| cr nn mmmmamaa 140103e20140103gw fot 00| 0|eng d 9783037196250 10.4171/125 doi DE-4084 PB bicssc 16Gxx msc 13Dxx msc 18Exx msc 20Cxx msc Benson edt Advances in Representation Theory of Algebras. EMS Press 2014 1 online resource (378 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 9 2523-5168 Restricted to subscribers. https://ems.press/books This volume presents a collection of articles devoted to representations of algebras and related topics. Dististinguished experts in this field presented their work at the International Conference on Representations of Algebras which took place 2012 in Bielefeld. Many of the expository surveys are included here. Researchers of representation theory will find in this volume interesting and stimulating contributions to the development of the subject. Mathematics bicssc Representation theory of associative rings and algebras msc Homological methods in commutative ring theory msc Categorical algebra msc Representation theory of groups msc Krause edt Skowroński edt https://ems.press/doi/10.4171/125 cover image https://content.ems.press/assets/public/images/books/cover-207.jpg nam a22 5a 4500 10.4171/131 DE-4084 2014-03-15 a fot 00| 0| cr nn mmmmamaa 140315e20140315gw fot 00| 0|eng d 9783037196311 10.4171/131 doi DE-4084 PBKJ bicssc 35Q55 msc 37K15 msc 37K10 msc 34L40 msc 34L20 msc Grébert aut The Defocusing NLS Equation and Its Normal Form. EMS Press 2014 1 online resource (175 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 18 2523-5184 Restricted to subscribers. https://ems.press/books The theme of this monograph is the nonlinear Schrödinger equation. This equation models slowly varying wave envelopes in dispersive media and arises in various physical systems such as water waves, plasma physics, solid state physics and nonlinear optics. More specifically, this book treats the defocusing nonlinear Schrödinger (dNLS) equation on the circle with a dynamical systems viewpoint. By developing the normal form theory it is shown that this equation is an integrable partial differential equation in the strongest possible sense. In particular, all solutions of the dNLS equation on the circle are periodic, quasi-periodic or almost-periodic in time and Hamiltonian perturbations of this equation can be studied near solutions far away from the equilibrium. The book is not only intended for specialists working at the intersection of integrable PDEs and dynamical systems, but also for researchers farther away from these fields as well as for graduate students. It is written in a modular fashion, each of its chapters and appendices can be read independently of each other. Differential calculus & equations bicssc NLS equations (nonlinear Schrödinger equations) msc Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems msc Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) msc Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) msc Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators msc Kappeler aut https://ems.press/doi/10.4171/131 cover image https://content.ems.press/assets/public/images/books/cover-205.jpg nam a22 5a 4500 10.4171/138 DE-4084 2014-05-10 a fot 00| 0| cr nn mmmmamaa 140510e20140510gw fot 00| 0|eng d 9783037196380 10.4171/138 doi DE-4084 PBM bicssc 51-01 msc 51N15 msc 51N10 msc 51N20 msc Casas-Alvero aut Analytic Projective Geometry. EMS Press 2014 1 online resource (636 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 14 2943-4955 Restricted to subscribers. https://ems.press/books Projective geometry is concerned with the properties of figures that are invariant by projecting and taking sections. It is considered one of the most beautiful parts of geometry and plays a central role because its specializations cover the whole of the affine, Euclidean and non-Euclidean geometries. The natural extension of projective geometry is projective algebraic geometry, a rich and active field of research. Regarding its applications, results and techniques of projective geometry are today intensively used in computer vision. This book contains a comprehensive presentation of projective geometry, over the real and complex number fields, and its applications to affine and Euclidean geometries. It covers central topics such as linear varieties, cross ratio, duality, projective transformations, quadrics and their classifications - projective, affine and metric -, as well as the more advanced and less usual spaces of quadrics, rational normal curves, line complexes and the classifications of collineations, pencils of quadrics and correlations. Two appendices are devoted to the projective foundations of perspective and to the projective models of plane non-Euclidean geometries. The presentation uses modern language, is based on linear algebra and provides complete proofs. Exercises are proposed at the end of each chapter; many of them are beautiful classical results. The material in this book is suitable for courses on projective geometry for undergraduate students, with a working knowledge of a standard first course on linear algebra. The text is a valuable guide to graduate students and researchers working in areas using or related to projective geometry, such as algebraic geometry and computer vision, and to anyone wishing to gain an advanced view on geometry as a whole. Geometry bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry msc Projective analytic geometry msc Affine analytic geometry msc Euclidean analytic geometry msc https://ems.press/doi/10.4171/138 cover image https://content.ems.press/assets/public/images/books/cover-211.jpg nam a22 5a 4500 10.4171/137 DE-4084 2014-04-28 a fot 00| 0| cr nn mmmmamaa 140428e20140428gw fot 00| 0|eng d 9783037196373 10.4171/137 doi DE-4084 PB bicssc PBC bicssc 00-02 msc 01-02 msc Deuflhard edt MATHEON - Mathematics for Key Technologies. EMS Press 2014 1 online resource (466 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series in Industrial and Applied Mathematics (esiam) 1 2523-5095 Restricted to subscribers. https://ems.press/books Mathematics: intellectual endeavor, production factor, key technology, key to key technologies? Mathematics is all of these The last three of its facets have been the focus of the research and development in the Berlin-based DFG Research Center MATHEON in the last twelve years. Through these activities MATHEON has become an international trademark for carrying out creative, application-driven research in mathematics and for cooperating with industrial partners in the solution of complex problems in key technologies. Modern key technologies have become highly sophisticated, integrating aspects of engineering, computer, business and other sciences. Flexible mathematical models, as well as fast and accurate methods for numerical simulation and optimization open new possibilities to handle the indicated complexities, to react quickly, and to explore new options. Researchers in mathematical fields such as Optimization, Discrete Mathematics, Numerical Analysis, Scientific Computing, Applied Analysis and Stochastic Analysis have to work hand in hand with scientists and engineers to fully exploit this potential and to strengthen the transversal role of mathematics in the solution of the challenging problems in key technologies. This book presents in seven chapters the highlights of the research work carried out in the MATHEON application areas: Life Sciences, Networks, Production, Electronic and Photonic Devices, Finance, Visualization, and Education. The chapters summarize many of the contributions, put them in the context of current mathematical research activities and outline their impact in various key technologies. To make some of the results more easily accessible to the general public, a large number of showcases are presented that illustrate a few success stories. Mathematics bicssc Mathematical foundations bicssc Research exposition (monographs, survey articles) pertaining to mathematics in general msc Research exposition (monographs, survey articles) pertaining to history and biography msc Grötschel edt Hömberg edt Horst edt Kramer edt Mehrmann edt Polthier edt Schmidt edt Schütte edt Skutella edt Sprekels edt https://ems.press/doi/10.4171/137 cover image https://content.ems.press/assets/public/images/books/cover-230.jpg nam a22 5a 4500 10.4171/117 DE-4084 2014-05-30 a fot 00| 0| cr nn mmmmamaa 140530e20140530gw fot 00| 0|eng d 9783037196175 10.4171/117 doi DE-4084 PBKD bicssc 30-00 msc 32-00 msc 57-00 msc 32G13 msc 32G15 msc 30F60 msc 11F06 msc 11F75 msc 14D20 msc 14H15 msc 14H60 msc 14H55 msc 14J60 msc 20F14 msc 20F28 msc 20F38 msc 20F65 msc 20F67 msc 20H10 msc 22E46 msc 30-03 msc 30C62 msc 30F20 msc 30F25 msc 30F10 msc 30F15 msc 30F30 msc 30F35 msc 30F40 msc 30F45 msc 32-03 msc 32S30 msc 53A35 msc 53B35 msc 53C35 msc 53C50 msc 53C80 msc 53D55 msc 53Z05 msc 57M07 msc 57M50 msc 57M60 msc 57N16 msc Papadopoulos edt Handbook of Teichmüller Theory, Volume IV. EMS Press 2014 1 online resource (838 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 19 2523-5141 Restricted to subscribers. https://ems.press/books Teichmüller theory is, since several decades, one of the most active research areas in mathematics, with a very wide range of points of view, including Riemann surface theory, hyperbolic geometry, low-dimensional topology, several complex variables, algebraic geometry, arithmetic, partial differential equations, dynamical systems, representation theory, symplectic geometry, geometric group theory, and mathematical physics. The present book is the fourth volume in a Handbook of Teichmüller Theory project that started as an attempt to present, in a most comprehensive and systematic way, the various aspects of this theory with its relations to all the fields mentioned. The handbook is addressed to researchers as well as graduate students. The present volume is divided into five parts: * Part A: The metric and the analytic theory. * Part B: Representation theory and generalized structures. * Part C: Dynamics. * Part D: The quantum theory. * Part E: Sources. Parts A, B and D are sequels of parts on the same theme in previous volumes. Part E has a new character in the series; it contains the translation together with a commentary of an important paper by Teichmüller which is almost unknown even to specialists. Making clear the original ideas of and motivations for a theory is crucial for many reasons, and rendering available this translation together with the commentary that follows will give a new impulse and will contribute in putting the theory into a broader perspective. The various volumes in this collection are written by experts who have a broad view on the subject. In general, the chapters have an expository character, which is the original purpose of this handbook, while some of them contain new and important results. Complex analysis, complex variables bicssc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functions of a complex variable msc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to several complex variables and analytic spaces msc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to manifolds and cell complexes msc Complex-analytic moduli problems msc Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) msc Teichmüller theory for Riemann surfaces msc Structure of modular groups and generalizations; arithmetic groups msc Cohomology of arithmetic groups msc Algebraic moduli problems, moduli of vector bundles msc Families, moduli of curves (analytic) msc Vector bundles on curves and their moduli msc Riemann surfaces; Weierstrass points; gap sequences msc Vector bundles on surfaces and higher-dimensional varieties, and their moduli msc Derived series, central series, and generalizations for groups msc Automorphism groups of groups msc Other groups related to topology or analysis msc Geometric group theory msc Hyperbolic groups and nonpositively curved groups msc Fuchsian groups and their generalizations (group-theoretic aspects) msc Semisimple Lie groups and their representations msc History of functions of a complex variable msc Quasiconformal mappings in the complex plane msc Classification theory of Riemann surfaces msc Ideal boundary theory for Riemann surfaces msc Compact Riemann surfaces and uniformization msc Harmonic functions on Riemann surfaces msc Differentials on Riemann surfaces msc Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) msc Kleinian groups (aspects of compact Riemann surfaces and uniformization) msc Conformal metrics (hyperbolic, Poincaré, distance functions) msc History of several complex variables and analytic spaces msc Deformations of complex singularities; vanishing cycles msc Non-Euclidean differential geometry msc Local differential geometry of Hermitian and Kählerian structures msc Differential geometry of symmetric spaces msc Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics msc Applications of global differential geometry to the sciences msc Deformation quantization, star products msc Applications of differential geometry to physics msc Topological methods in group theory msc General geometric structures on low-dimensional manifolds msc Group actions on manifolds and cell complexes in low dimensions msc Geometric structures on manifolds of high or arbitrary dimension msc https://ems.press/doi/10.4171/117 cover image https://content.ems.press/assets/public/images/books/cover-231.png nam a22 5a 4500 10.4171/134 DE-4084 2014-07-01 a fot 00| 0| cr nn mmmmamaa 140701e20140701gw fot 00| 0|eng d 9783037196342 10.4171/134 doi DE-4084 PBKJ bicssc 58J05 msc 35J15 msc Hebey aut Compactness and Stability for Nonlinear Elliptic Equations. EMS Press 2014 1 online resource (301 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 20 2943-4971 Restricted to subscribers. https://ems.press/books The book offers an expanded version of lectures given at ETH Zürich in the framework of a Nachdiplomvorlesung. Compactness and stability for nonlinear elliptic equations in the inhomogeneous context of closed Riemannian manifolds are investigated, a field presently undergoing great development. The author describes blow-up phenomena and presents the progress made over the past years on the subject, giving an up-to-date description of the new ideas, concepts, methods, and theories in the field. Special attention is devoted to the nonlinear stationary Schrödinger equation and to its critical formulation. Intended to be as self-contained as possible, the book is accessible to a broad audience of readers, including graduate students and researchers. Differential calculus & equations bicssc Elliptic equations on manifolds, general theory msc Second-order elliptic equations msc https://ems.press/doi/10.4171/134 cover image https://content.ems.press/assets/public/images/books/cover-195.png nam a22 5a 4500 10.4171/133 DE-4084 2014-07-07 a fot 00| 0| cr nn mmmmamaa 140707e20140707gw fot 00| 0|eng d 9783037196335 10.4171/133 doi DE-4084 PBT bicssc 60-01 msc 60G07 msc 60J60 msc 60J65 msc 60H05 msc 60H07 msc Baudoin aut Diffusion Processes and Stochastic Calculus. EMS Press 2014 1 online resource (287 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 15 2943-4955 Restricted to subscribers. https://ems.press/books The main purpose of the book is to present at a graduate level and in a self-contained way the most important aspects of the theory of continuous stochastic processes in continuous time and to introduce to some of its ramifications like the theory of semigroups, the Malliavin calculus and the Lyons rough paths. It is intended for students, or even researchers, who wish to learn the basics in a concise but complete and rigorous manner. Several exercises are distributed throughout the text to test the understanding of the reader and each chapter ends up with bibliographic comments aimed to those interested in exploring further the materials. The stochastic calculus has been developed in the 1950s and the range of its applications is huge and still growing today. Besides being a fundamental component of modern probability theory, domains of applications include but are not limited to: mathematical finance, biology, physics, and engineering sciences. The first part of the text is devoted the general theory of stochastic processes, we focus on existence and regularity results for processes and on the theory of martingales. This allows to quickly introduce the Brownian motion and to study its most fundamental properties. The second part deals with the study of Markov processes, in particular diffusions. Our goal is to stress the connections between these processes and the theory of evolution semigroups. The third part deals with stochastic integrals, stochastic differential equations and Malliavin calculus. Finally, in the fourth and final part we present an introduction to the very new theory of rough paths by Terry Lyons. Probability & statistics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory msc General theory of stochastic processes msc Diffusion processes msc Brownian motion msc Stochastic integrals msc Stochastic calculus of variations and the Malliavin calculus msc https://ems.press/doi/10.4171/133 cover image https://content.ems.press/assets/public/images/books/cover-196.png nam a22 5a 4500 10.4171/149 DE-4084 2014-09-01 a fot 00| 0| cr nn mmmmamaa 140901e20140901gw fot 00| 0|eng d 9783037196496 10.4171/149 doi DE-4084 PB bicssc 12E30 msc 12F10 msc 13A18 msc 14H20 msc 14M25 msc 11U09 msc 12E05 msc 12F05 msc 12L12 msc 13D40 msc 13F30 msc 13H05 msc 13N15 msc 14C20 msc 14F10 msc 14J17 msc 16W60 msc 32P05 msc 37A05 msc 54F50 msc Campillo edt Valuation Theory in Interaction. EMS Press 2014 1 online resource (670 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 10 2523-5168 Restricted to subscribers. https://ems.press/books Having its classical roots, since more than a century, in algebraic number theory, algebraic geometry and the theory of ordered fields and groups, valuation theory has seen an amazing expansion into many other areas in recent decades. Moreover, having been dormant for a while in algebraic geometry, it has now been reintroduced as a tool to attack the open problem of resolution of singularities in positive characteristic and to analyse the structure of singularities. Driven by this topic, and by its many new applications in other areas, also the research in valuation theory itself has been intensified, with a particular emphasis on the deep open problems in positive characteristic. As important examples for the expansion of valuation theory, it has become extremely useful in the theory of complex dynamical systems, and in the study of non-oscillating trajectories of real analytic vector fields in three dimensions. Analogues of the Riemann-Zariski valuation spaces have been found to be the proper framework for questions of intersection theory in algebraic geometry and in the analysis of singularities of complex plurisubharmonic functions. In a different direction, the relation between Berkovich geometry, tropical geometry and valuation spaces, on the one hand, and the geometry of arc spaces and valuation spaces, on the other, have begun to deepen and clarify. Ever since its beginnings, valuation theory and Galois theory have grown closely together and influenced each other. Arguably, studying and understanding the extensions of valuations in algebraic field extensions is one of the most important questions in valuation theory, whereas using valuation theory is one of he most important tools in studying Galois extensions of fields, as well as constructing field extensions with given properties. The well established topic of the model theory of valued fields is also being transformed, in particular through the study of valued fields with functions and operators, and through the study of types over valued fields. The multifaceted development of valuation theory has been monitored by two International Conferences and Workshops: the first in 1999 in Saskatoon, Canada, and the second in 2011 in Segovia and El Escorial in Spain. This book grew out of the second conference and presents high quality papers on recent research together with survey papers that illustrate the state of the art in several areas and applications of valuation theory. The book is addressed to researchers and graduate students who work in valuation theory or the areas where it is applied, as well as a general mathematical audience interested in the expansion and usefulness of the valuation theoretical approach, which has been called the most analytic form of algebraic reasoning. For young mathematicians who want to enter these areas of research, it provides a valuable source of up-to-date information. Mathematics bicssc Field arithmetic msc Separable extensions, Galois theory msc Valuations and their generalizations for commutative rings msc Singularities of curves, local rings msc Toric varieties, Newton polyhedra, Okounkov bodies msc Model theory (number-theoretic aspects) msc Polynomials in general fields (irreducibility, etc.) msc Algebraic field extensions msc Model theory of fields msc Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series msc Valuation rings msc Regular local rings msc Derivations and commutative rings msc Divisors, linear systems, invertible sheaves msc Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials msc Singularities of surfaces or higher-dimensional varieties msc Valuations, completions, formal power series and related constructions (associative rings and algebras) msc Non-Archimedean analysis msc Dynamical aspects of measure-preserving transformations msc Topological spaces of dimension \(\leq 1\); curves, dendrites msc Kuhlmann edt Teissier edt https://ems.press/doi/10.4171/149 cover image https://content.ems.press/assets/public/images/books/cover-197.png nam a22 5a 4500 10.4171/141 DE-4084 2014-08-12 a fot 00| 0| cr nn mmmmamaa 140812e20140812gw fot 00| 0|eng d 9783037196410 10.4171/141 doi DE-4084 PBK bicssc 58B20 msc 58B25 msc 58B34 msc 53C55 msc 53D50 msc Sergeev aut Lectures on Universal Teichmüller Space. EMS Press 2014 1 online resource (111 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 19 2523-5184 Restricted to subscribers. https://ems.press/books This book is based on a lecture course given by the author at the Educational Center of Steklov Mathematical Institute in 2011. It is designed for a one semester course for undergraduate students, familiar with basic differential geometry, complex and functional analysis. The universal Teichmüller space \mathcal T is the quotient of the space of quasisymmetric homeomorphisms of the unit circle modulo Möbius transformations. The first part of the book is devoted to the study of geometric and analytic properties of \mathcal T. It is an infinite-dimensional Kähler manifold which contains all classical Teichmüller spaces of compact Riemann surfaces as complex submanifolds which explains the name universal Teichmüller space. Apart from classical Teichmüller spaces, \mathcal T contains the space \mathcal S of diffeomorphisms of the circle modulo Möbius transformations. The latter space plays an important role in the quantization of the theory of smooth strings. The quantization of \mathcal T is presented in the second part of the book. In contrast with the case of diffeomorphism space \mathcal S, which can be quantized in frames of the conventional Dirac scheme, the quantization of \mathcal T requires an absolutely different approach based on the noncommutative geometry methods. The book concludes with a list of 24 problems and exercises which can be used during the examinations. Calculus & mathematical analysis bicssc Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds msc Group structures and generalizations on infinite-dimensional manifolds msc Noncommutative geometry (à la Connes) msc Global differential geometry of Hermitian and Kählerian manifolds msc Geometric quantization msc https://ems.press/doi/10.4171/141 cover image https://content.ems.press/assets/public/images/books/cover-199.png nam a22 5a 4500 10.4171/147 DE-4084 2014-12-01 a fot 00| 0| cr nn mmmmamaa 141201e20141201gw fot 00| 0|eng d 9783037196472 10.4171/147 doi DE-4084 PBMP bicssc 01A55 msc 35Q53 msc 37D25 msc 37D20 msc 37D40 msc 47H09 msc 51-00 msc 51-02 msc 51-03 msc 51A05 msc 51B20 msc 51F99 msc 51K05 msc 51K10 msc 51K99 msc 51M10 msc 52A07 msc 52A20 msc 52A99 msc 53A20 msc 53A35 msc 53B40 msc 53C22 msc 53C24 msc 53C60 msc 53C70 msc 57S25 msc 58-00 msc 58-02 msc 58-03 msc 58B20 msc 58D05 msc Papadopoulos edt Handbook of Hilbert Geometry. EMS Press 2014 1 online resource (460 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 22 2523-5141 Restricted to subscribers. https://ems.press/books This volume presents surveys, written by experts in the field, on various classical and the modern aspects of Hilbert geometry. They are assuming several points of view: Finsler geometry, calculus of variations, projective geometry, dynamical systems, and others. Some fruitful relations between Hilbert geometry and other subjects in mathematics are emphasized, including Teichmüller spaces, convexity theory, Perron-Frobenius theory, representation theory, partial differential equations, coarse geometry, ergodic theory, algebraic groups, Coxeter groups, geometric group theory, Lie groups and discrete group actions. The _Handbook_ is addressed to both students who want to learn the theory and researchers working in the area. Differential & Riemannian geometry bicssc History of mathematics in the 19th century msc KdV equations (Korteweg-de Vries equations) msc Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) msc Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) msc Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) msc Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. msc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to geometry msc Research exposition (monographs, survey articles) pertaining to geometry msc History of geometry msc General theory of linear incidence geometry and projective geometries msc Minkowski geometries in nonlinear incidence geometry msc Metric geometry msc General theory of distance geometry msc Synthetic differential geometry msc Distance geometry msc Hyperbolic and elliptic geometries (general) and generalizations msc Convex sets in topological vector spaces (aspects of convex geometry) msc Convex sets in \(n\) dimensions (including convex hypersurfaces) msc General convexity msc Projective differential geometry msc Non-Euclidean differential geometry msc Local differential geometry of Finsler spaces and generalizations (areal metrics) msc Geodesics in global differential geometry msc Rigidity results msc Global differential geometry of Finsler spaces and generalizations (areal metrics) msc Direct methods (\(G\)-spaces of Busemann, etc.) msc Groups acting on specific manifolds msc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to global analysis msc Research exposition (monographs, survey articles) pertaining to global analysis msc History of global analysis msc Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds msc Groups of diffeomorphisms and homeomorphisms as manifolds msc Troyanov edt https://ems.press/doi/10.4171/147 cover image https://content.ems.press/assets/public/images/books/cover-200.png nam a22 5a 4500 10.4171/150 DE-4084 2015-01-15 a fot 00| 0| cr nn mmmmamaa 150115e20150115gw fot 00| 0|eng d 9783037196502 10.4171/150 doi DE-4084 PBKJ bicssc 46-02 msc 46E35 msc 42B35 msc 42C40 msc 35K05 msc 35Q30 msc 76D03 msc 76D05 msc Triebel aut Hybrid Function Spaces, Heat and Navier-Stokes Equations. EMS Press 2015 1 online resource (196 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 24 2943-5005 Restricted to subscribers. https://ems.press/books This book is the continuation of _Local Function Spaces, Heat and Navier-Stokes Equations_ (Tracts in Mathematics 20, 2013) by the author. A new approach is presented to exhibit relations between Sobolev spaces, Besov spaces, and Hölder-Zygmund spaces on the one hand and Morrey-Campanato spaces on the other. Morrey-Campanato spaces extend the notion of functions of bounded mean oscillation. These spaces play a crucial role in the theory of linear and nonlinear PDEs. Chapter 1 (Introduction) describes the main motivations and intentions of this book. Chapter 2 is a selfcontained introduction into Morrey spaces. Chapter 3 deals with hybrid smoothness spaces (which are between local and global spaces) in Euclidean n-space based on the Morrey-Campanato refinement of the Lebesgue spaces. The presented approach relies on wavelet decompositions. This is applied in Chapter 4 to linear and nonlinear heat equations in global and hybrid spaces. The obtained assertions about function spaces and nonlinear heat equations are used in the Chapters 5 and 6 to study Navier-Stokes equations in hybrid and global spaces. This book is addressed to graduate students and mathematicians having a working knowledge of basic elements of (global) function spaces, and who are interested in applications to nonlinear PDEs with heat and Navier-Stokes equations as prototypes. Differential calculus & equations bicssc Research exposition (monographs, survey articles) pertaining to functional analysis msc Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems msc Function spaces arising in harmonic analysis msc Nontrigonometric harmonic analysis involving wavelets and other special systems msc Heat equation msc Navier-Stokes equations msc Existence, uniqueness, and regularity theory for incompressible viscous fluids msc Navier-Stokes equations for incompressible viscous fluids msc https://ems.press/doi/10.4171/150 cover image https://content.ems.press/assets/public/images/books/cover-202.jpg nam a22 5a 4500 10.4171/151 DE-4084 2015-02-18 a fot 00| 0| cr nn mmmmamaa 150218e20150218gw fot 00| 0|eng d 9783037196519 10.4171/151 doi DE-4084 PBK bicssc 58J35 msc 58J37 msc 58J50 msc 58J53 msc 35P05 msc 35P15 msc 35P20 msc 47A05 msc 47A10 msc 47A12 msc 47A60 msc 47A75 msc 49R05 msc 53C21 msc Lablée aut Spectral Theory in Riemannian Geometry. EMS Press 2015 1 online resource (197 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 16 2943-4955 Restricted to subscribers. https://ems.press/books Spectral theory is a diverse area of mathematics that derives its motivations, goals and impetus from several sources. In particular, the spectral theory of the Laplacian on a compact Riemannian manifold is a central object in differential geometry. From a physical point a view, the Laplacian on a compact Riemannian manifold is a fundamental linear operator which describes numerous propagation phenomena: heat propagation, wave propagation, quantum dynamics, etc. Moreover, the spectrum of the Laplacian contains vast information about the geometry of the manifold. This book gives a self-containded introduction to spectral geometry on compact Riemannian manifolds. Starting with an overview of spectral theory on Hilbert spaces, the book proceeds to a description of the basic notions in Riemannian geometry. Then its makes its way to topics of main interests in spectral geometry. The topics presented include direct and inverse problems. Direct problems are concerned with computing or finding properties on the eigenvalues while the main issue in inverse problems is knowing the spectrum of the Laplacian, can we determine the geometry of the manifold? Addressed to students or young researchers, the present book is a first introduction in spectral theory applied to geometry. For readers interested in pursuing the subject further, this book will provide a basis for understanding principles, concepts and developments of spectral geometry. Calculus & mathematical analysis bicssc Heat and other parabolic equation methods for PDEs on manifolds msc Perturbations of PDEs on manifolds; asymptotics msc Spectral problems; spectral geometry; scattering theory on manifolds msc Isospectrality msc General topics in linear spectral theory for PDEs msc Estimates of eigenvalues in context of PDEs msc Asymptotic distributions of eigenvalues in context of PDEs msc General (adjoints, conjugates, products, inverses, domains, ranges, etc.) msc Spectrum, resolvent msc Numerical range, numerical radius msc Functional calculus for linear operators msc Eigenvalue problems for linear operators msc Variational methods for eigenvalues of operators msc Methods of global Riemannian geometry, including PDE methods; curvature restrictions msc https://ems.press/doi/10.4171/151 cover image https://content.ems.press/assets/public/images/books/cover-204.jpg nam a22 5a 4500 10.4171/152 DE-4084 2015-03-20 a fot 00| 0| cr nn mmmmamaa 150320e20150320gw fot 00| 0|eng d 9783037196526 10.4171/152 doi DE-4084 PB bicssc 82B05 msc 82B21 msc 82B26 msc 15B52 msc 82D55 msc 35A15 msc 35J20 msc 35J60 msc Serfaty aut Coulomb Gases and Ginzburg-Landau Vortices. EMS Press 2015 1 online resource (165 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 21 2943-4971 Restricted to subscribers. https://ems.press/books The topic of this book is systems of points in Coulomb interaction, in particular, the classical Coulomb gas, and vortices in the Ginzburg-Landau model of superconductivity. The classical Coulomb and Log gases are classical statistical mechanics models, which have seen important developments in the mathematical literature due to their connection with random matrices and approximation theory. At low temperature, these systems are expected to cristallize to so-called Fekete sets, which exhibit microscopically a lattice structure. The Ginzburg-Landau model, on the other hand, describes superconductors. In superconducting materials subjected to an external magnetic field, densely packed point vortices emerge, forming perfect triangular lattice patterns, so-called Abrikosov lattices. This book describes these two systems and explores the similarity between them. It presents the mathematical tools developed to analyze the interaction between the Coulomb particles or the vortices, at the microscopic scale, and describes a renormalized energy governing the point patterns. This is believed to measure the disorder of a point configuration, and to be minimized by the Abrikosov lattice in dimension 2. The book gives a self-contained presentation of results on the mean field limit of the Coulomb gas system, with or without temperature, and of the derivation of the renormalized energy. It also provides a streamlined presentation of the similar analysis that can be performed for the Ginzburg-Landau model, including a review of the vortex-specific tools and the derivation of the critical fields, the mean-field limit and the renormalized energy. Mathematics bicssc Classical equilibrium statistical mechanics (general) msc Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics msc Phase transitions (general) in equilibrium statistical mechanics msc Random matrices (algebraic aspects) msc Statistical mechanics of superconductors msc Variational methods applied to PDEs msc Variational methods for second-order elliptic equations msc Nonlinear elliptic equations msc https://ems.press/doi/10.4171/152 cover image https://content.ems.press/assets/public/images/books/cover-208.jpg nam a22 5a 4500 10.4171/146 DE-4084 2015-03-31 a fot 00| 0| cr nn mmmmamaa 150331e20150331gw fot 00| 0|eng d 9783037196465 10.4171/146 doi DE-4084 PBX bicssc 01A60 msc 01A70 msc 11R37 msc 11R39 msc 11S37 msc 11Fxx msc 11Mxx msc Dumbaugh aut Emil Artin and Beyond - Class Field Theory and L-Functions. EMS Press 2015 1 online resource (245 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 9 2523-5222 Restricted to subscribers. https://ems.press/books This book explores the development of number theory, and class field theory in particular, as it passed through the hands of Emil Artin, Claude Chevalley and Robert Langlands in the middle of the twentieth century. Claude Chevalleys presence in Artins 1931 Hamburg lectures on class field theory serves as the starting point for this volume. From there, it is traced how class field theory advanced in the 1930s and how Artins contributions influenced other mathematicians at the time and in subsequent years. Given the difficult political climate and his forced emigration as it were, the question of how Artin created a life in America within the existing institutional framework, and especially of how he continued his education of and close connection with graduate students, is considered. In particular, Artins collaboration in algebraic number theory with George Whaples and his student Margaret Matchetts thesis work On the zeta-function for ideles in the 1940s are investigated. A (first) study of the influence of Artin on present day work on a non-abelian class field theory finishes the book. The volume consists of individual essays by the authors and two contributors, James Cogdell and Robert Langlands, and contains relevant archival material. Among these, the letter from Chevalley to Helmut Hasse in 1935 is included, where he introduces the notion of ideles and explores their significance, along with the previously unpublished thesis by Matchett and the seminal letter of Langlands to André Weil of 1967 where he lays out his ideas regarding a non-abelian class field theory. Taken together, these chapters offer a view of both the life of Artin in the 1930s and 1940s and the development of class field theory at that time. They also provide insight into the transmission of mathematical ideas, the careful steps required to preserve a life in mathematics at a difficult moment in history, and the interplay between mathematics and politics (in more ways than one). Some of the technical points in this volume require a sophisticated understanding of algebra and number theory. The broader topics, however, will appeal to a wider audience that extends beyond mathematicians and historians of mathematics to include historically minded individuals, particularly those with an interest in the time period. History of mathematics bicssc History of mathematics in the 20th century msc Biographies, obituaries, personalia, bibliographies msc Class field theory msc Langlands-Weil conjectures, nonabelian class field theory msc Langlands-Weil conjectures, nonabelian class field theory msc Discontinuous groups and automorphic forms msc Zeta and \(L\)-functions: analytic theory msc Schwermer aut https://ems.press/doi/10.4171/146 cover image https://content.ems.press/assets/public/images/books/cover-209.jpg nam a22 5a 4500 10.4171/144 DE-4084 2015-04-10 a fot 00| 0| cr nn mmmmamaa 150410e20150410gw fot 00| 0|eng d 9783037196441 10.4171/144 doi DE-4084 PBX bicssc 01A60 msc 01A70 msc 11R37 msc 11R39 msc 11S37 msc 11Fxx msc 11Mxx msc Bečvářová aut Karl Löwner and His Student Lipman Bers - Pre-war Prague Mathematicians. EMS Press 2015 1 online resource (310 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 10 2523-5222 Restricted to subscribers. https://ems.press/books This monograph is devoted to two distinguished mathematicians, Karel Löwner (1893-1968) and Lipman Bers (1914-1993), whose lives are dramatically interlinked with key historical events of the 20th century. K. Löwner, Professor of Mathematics at the German University in Prague (Czechoslovakia), was dismissed from his position because he was a Jew, and emigrated to the USA in 1939 (where he changed his name to Charles Loewner). Earlier, he had published several outstanding papers in complex analysis and a masterpiece on matrix functions. In particular, his ground-breaking parametric method in geometric function theory from 1923, which led to Löwners celebrated differential equation, brought him world-wide fame and turned out to be a cornerstone in de Branges proof of the Bieberbach conjecture. Unexpectedly, Löwners differential equation has gained recent prominence with the introduction of a conformally invariant stochastic process called stochastic Loewner evolution (SLE) by O. Schramm in 2000. SLE features in two Fields Medal citations from 2006 and 2010. L. Bers was the final Prague Ph.D. student of K. Löwner. His dissertation on potential theory (1938), completed shortly before his emigration and long thought to be irretrievably lost, was found in 2006. It is here made accessible for the first time, with an extensive commentary, to the mathematical community. This monograph presents an in-depth account of the lives of both mathematicians, with special emphasis on the pre-war period. Löwners teaching activities and professional achievements are presented in the context of the prevailing complex political situation and against the background of the wider development of mathematics in Europe. Each of his publications is accompanied by an extensive commentary, tracing the origin and motivation of the problem studied, and describing the state-of-art at the time of the corresponding mathematical field. Special attention is paid to the impact of the results obtained and to the later development of the underlying ideas, thus connecting Löwners achievements to current research activity. The text is based on an extensive archival search, and most of the archival findings appear here for the first time. Anyone with an interest in mathematics and the history of mathematics will enjoy reading this book about two famous mathematicians of the 20th century. History of mathematics bicssc History of mathematics in the 20th century msc Biographies, obituaries, personalia, bibliographies msc Class field theory msc Langlands-Weil conjectures, nonabelian class field theory msc Langlands-Weil conjectures, nonabelian class field theory msc Discontinuous groups and automorphic forms msc Zeta and \(L\)-functions: analytic theory msc Netuka aut https://ems.press/doi/10.4171/144 cover image https://content.ems.press/assets/public/images/books/cover-210.jpg nam a22 5a 4500 10.4171/153 DE-4084 2015-09-30 a fot 00| 0| cr nn mmmmamaa 150930e20150930gw fot 00| 0|eng d 9783037196533 10.4171/153 doi DE-4084 PBMP bicssc PBPD bicssc 53D40 msc 53D12 msc 53D25 msc 53D35 msc 53D37 msc 55P35 msc 55P50 msc 55P62 msc 55P92 msc 13D03 msc 13D07 msc 13D09 msc 13D10 msc 16E40 msc 16E45 msc 57R15 msc 57R19 msc 57R56 msc 57R70 msc 57R91 msc Latschev edt Free Loop Spaces in Geometry and Topology ; Including the monograph Symplectic cohomology and Viterbos theorem by Mohammed Abouzaid. EMS Press 2015 1 online resource (500 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 24 2523-5141 Restricted to subscribers. https://ems.press/books In the late 1990s two initially unrelated developments brought free loop spaces into renewed focus. In 1999, Chas and Sullivan introduced a wealth of new algebraic operations on the homology of these spaces under the name of _string topology_, the full scope of which is still not completely understood. A few years earlier, Viterbo had discovered a first deep link between the _symplectic topology_ of cotangent bundles and the topology of their free loop space. In the past 15 years, many exciting connections between these two viewpoints have been found. Still, researchers working on one side of the story often know quite little about the other. One of the main purposes of this book is to facilitate communication between topologists and symplectic geometers thinking about free loop spaces. It was written by active researchers coming to the topic from both perspectives and provides a concise overview of many of the classical results, while also beginning to explore the new directions of research that have emerged recently. As one highlight, it contains a research monograph by M. Abouzaid which proves a strengthened version of Viterbos isomorphism between the homology of the free loop space of a manifold and the symplectic cohomology of its cotangent bundle, following a new strategy. The book grew out of a learning seminar on free loop spaces held at Strasbourg University in 2008-2009, and should be accessible to a graduate student with a general interest in the topic. It focuses on introducing and explaining the most important aspects rather than offering encyclopedic coverage, while providing the interested reader with a broad basis for further studies and research. Differential & Riemannian geometry bicssc Algebraic topology bicssc Symplectic aspects of Floer homology and cohomology msc Lagrangian submanifolds; Maslov index msc Geodesic flows in symplectic geometry and contact geometry msc Global theory of symplectic and contact manifolds msc Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category msc Loop spaces msc String topology msc Rational homotopy theory msc Relations between equivariant and nonequivariant homotopy theory in algebraic topology msc (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) msc Homological functors on modules of commutative rings (Tor, Ext, etc.) msc Derived categories and commutative rings msc Deformations and infinitesimal methods in commutative ring theory msc (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) msc Differential graded algebras and applications (associative algebraic aspects) msc Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) msc Algebraic topology on manifolds and differential topology msc Topological quantum field theories (aspects of differential topology) msc Critical points and critical submanifolds in differential topology msc Equivariant algebraic topology of manifolds msc Oancea edt https://ems.press/doi/10.4171/153 cover image https://content.ems.press/assets/public/images/books/cover-212.jpg nam a22 5a 4500 10.4171/148 DE-4084 2015-04-30 a fot 00| 0| cr nn mmmmamaa 150430e20150430gw fot 00| 0|eng d 9783037196489 10.4171/148 doi DE-4084 PBX bicssc PBM bicssc 01-00 msc 01-02 msc 01A05 msc 01A55 msc 01A70 msc 22-00 msc 22-02 msc 22-03 msc 51N15 msc 51P05 msc 53A20 msc 53A35 msc 53B50 msc 54H15 msc 58E40 msc Ji edt Sophus Lie and Felix Klein: The Erlangen Program and Its Impact in Mathematics and Physics. EMS Press 2015 1 online resource (348 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 23 2523-5141 Restricted to subscribers. https://ems.press/books The Erlangen program expresses a fundamental point of view on the use of groups and transformation groups in mathematics and physics. The present volume is the first modern comprehensive book on that program and its impact in contemporary mathematics and physics. Klein spelled out the program, and Lie, who contributed to its formulation, is the first mathematician who made it effective in his work. The theories that these two authors developed are also linked to their personal history and to their relations with each other and with other mathematicians, incuding Hermann Weyl, Élie Cartan, Henri Poincaré, and many others. All these facets of the Erlangen program appear in the present volume. The book is written by well-known experts in geometry, physics and history of mathematics and physics. It is addressed to mathematicians, to graduate students, and to all those interested in the development of mathematical ideas. History of mathematics bicssc Geometry bicssc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to history and biography msc Research exposition (monographs, survey articles) pertaining to history and biography msc General histories, source books msc History of mathematics in the 19th century msc Biographies, obituaries, personalia, bibliographies msc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to topological groups msc Research exposition (monographs, survey articles) pertaining to topological groups msc History of topological groups msc Projective analytic geometry msc Classical or axiomatic geometry and physics msc Projective differential geometry msc Non-Euclidean differential geometry msc Applications of local differential geometry to the sciences msc Transformation groups and semigroups (topological aspects) msc Variational aspects of group actions in infinite-dimensional spaces msc Papadopoulos edt https://ems.press/doi/10.4171/148 cover image https://content.ems.press/assets/public/images/books/cover-213.jpg nam a22 5a 4500 10.4171/139 DE-4084 2015-06-01 a fot 00| 0| cr nn mmmmamaa 150601e20150601gw fot 00| 0|eng d 9783037196397 10.4171/139 doi DE-4084 PB bicssc 20Fxx msc 20F05 msc 20F10 msc 20F36 msc 20F60 msc 20F65 msc 20M05 msc 20M10 msc 05A05 msc 18B40 msc 18G35 msc 20B30 msc 20F55 msc 20L05 msc 20M50 msc 20N02 msc 68Q17 msc Dehornoy aut Foundations of Garside Theory. EMS Press 2015 1 online resource (710 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 22 2943-5005 Restricted to subscribers. https://ems.press/books **Winner of the 2014 EMS Monograph Award** This text is a monograph in algebra, with connections toward geometry and low-dimensional topology. It mainly involves groups, monoids, and categories, and aims at providing a unified treatment for those situations in which one can find distinguished decompositions by iteratively extracting a maximal fragment lying in a prescribed family. Initiated in 1969 by F. A. Garside in the case of Artins braid groups, this approach turned out to lead to interesting results in a number of cases, the central notion being what the authors call a Garside family. At the moment, the study is far from complete, and the purpose of this book is both to present the current state of the theory and to be an invitation for further research. There are two parts: the bases of a general theory, including many easy examples, are developed in Part A, whereas various more sophisticated examples are specifically addressed in Part B. In order to make the content accessible to a wide audience of nonspecialists, exposition is essentially self-contained and very few prerequisites are needed. In particular, it should be easy to use the current text as a textbook both for Garside theory and for the more specialized topics investigated in Part B: Artin-Tits groups, Deligne-Lusztig varieties, groups of algebraic laws, ordered groups, structure groups of set-theoretic solutions of the Yang-Baxter equation. The first part of the book can be used as the basis for a graduate or advanced undergraduate course. Mathematics bicssc Special aspects of infinite or finite groups msc Generators, relations, and presentations of groups msc Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) msc Braid groups; Artin groups msc Ordered groups (group-theoretic aspects) msc Geometric group theory msc Free semigroups, generators and relations, word problems msc General structure theory for semigroups msc Permutations, words, matrices msc Groupoids, semigroupoids, semigroups, groups (viewed as categories) msc Chain complexes (category-theoretic aspects), dg categories msc Symmetric groups msc Reflection and Coxeter groups (group-theoretic aspects) msc Groupoids (i.e. small categories in which all morphisms are isomorphisms) msc Connections of semigroups with homological algebra and category theory msc Sets with a single binary operation (groupoids) msc Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) msc Digne aut Godelle aut Krammer aut Michel aut https://ems.press/doi/10.4171/139 cover image https://content.ems.press/assets/public/images/books/cover-214.jpg nam a22 5a 4500 10.4171/143 DE-4084 2015-06-30 a fot 00| 0| cr nn mmmmamaa 150630e20150630gw fot 00| 0|eng d 9783037196434 10.4171/143 doi DE-4084 PBV bicssc 06A07 msc 16T05 msc 41A58 msc 58D05 msc 93C10 msc 05C05 msc 81T18 msc 34A25 msc 34M25 msc 47H20 msc 65L05 msc 81T15 msc 81T16 msc Ebrahimi-Fard edt Faà di Bruno Hopf Algebras, Dyson-Schwinger Equations, and Lie-Butcher Series. EMS Press 2015 1 online resource (466 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 21 2523-5141 Restricted to subscribers. https://ems.press/books Since the early works of G.-C. Rota and his school, Hopf algebras have been instrumental in algebraic combinatorics. In a seminal 1998 paper, A. Connes and D. Kreimer presented a Hopf algebraic approach to renormalization in perturbative Quantum Field Theory (QFT). This work triggered an abundance of new research on applications of Hopf algebraic techniques in QFT as well as other areas of theoretical physics. Furthermore, these new developments were complemented by progress made in other domains of applications, such as control theory, dynamical systems, and numerical integration methods. Especially in the latter context, it became clear that J. Butchers work from the early 1970s was well ahead of its time. The present volume emanated from a conference hosted in June 2011 by IRMA at Strasbourg University in France. Researchers from different scientific communities who share similar techniques and objectives gathered at this meeting to discuss new ideas and results on Faà di Bruno algebras, Dyson-Schwinger equations, and Butcher series. The purpose of this book is to present a coherent set of lectures reflecting the state of the art of research on combinatorial Hopf algebras relevant to high energy physics, control theory, dynamical systems, and numerical integration methods. More specifically, connections between Dyson-Schwinger equations, Faà di Bruno algebras, and Butcher series are examined in great detail. This volume is aimed at researchers and graduate students interested in combinatorial and algebraic aspects of QFT, control theory, dynamical systems and numerical analysis of integration methods. It contains introductory lectures on the various constructions that are emerging and developing in these domains. Combinatorics & graph theory bicssc Combinatorics of partially ordered sets msc Hopf algebras and their applications msc Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) msc Groups of diffeomorphisms and homeomorphisms as manifolds msc Nonlinear systems in control theory msc Trees msc Feynman diagrams msc Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. msc Formal solutions and transform techniques for ordinary differential equations in the complex domain msc Semigroups of nonlinear operators msc Numerical methods for initial value problems involving ordinary differential equations msc Perturbative methods of renormalization applied to problems in quantum field theory msc Nonperturbative methods of renormalization applied to problems in quantum field theory msc Fauvet edt https://ems.press/doi/10.4171/143 cover image https://content.ems.press/assets/public/images/books/cover-215.jpg nam a22 5a 4500 10.4171/136 DE-4084 2015-06-29 a fot 00| 0| cr nn mmmmamaa 150629e20150629gw fot 00| 0|eng d 9783037196366 10.4171/136 doi DE-4084 PBMP bicssc PBKJ bicssc 53C27 msc 53C26 msc 53C55 msc 53C80 msc 17B10 msc 34L40 msc 35S05 msc Bourguignon aut A Spinorial Approach to Riemannian and Conformal Geometry. EMS Press 2015 1 online resource (462 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Monographs in Mathematics (emm) 6 2523-5206 Restricted to subscribers. https://ems.press/books The book gives an elementary and comprehensive introduction to Spin Geometry, with particular emphasis on the Dirac operator which plays a fundamental role in differential geometry and mathematical physics. After a self-contained presentation of the basic algebraic, geometrical, analytical and topological ingredients, a systematic study of the spectral properties of the Dirac operator on compact spin manifolds is carried out. The classical estimates on eigenvalues and their limiting cases are discussed next, highlighting the subtle interplay of spinors and special geometric structures. Several applications of these ideas are presented, including spinorial proofs of the Positive Mass Theorem or the classification of positive Kähler-Einstein contact manifolds. Representation theory is used to explicitly compute the Dirac spectrum of compact symmetric spaces. The special features of the book include a unified treatment of Spin^\mathrm c and conformal spin geometry (with special emphasis on the conformal covariance of the Dirac operator), an overview with proofs of the theory of elliptic differential operators on compact manifolds based on pseudodifferential calculus, a spinorial characterization of special geometries, and a self-contained presentation of the representation-theoretical tools needed in order to apprehend spinors. This book will help advanced graduate students and researchers to get more familiar with this beautiful, though not sufficiently known, domain of mathematics with great relevance to both theoretical physics and geometry. Differential & Riemannian geometry bicssc Differential calculus & equations bicssc Spin and Spin\({}^c\) geometry msc Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry msc Global differential geometry of Hermitian and Kählerian manifolds msc Applications of global differential geometry to the sciences msc Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) msc Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) msc Pseudodifferential operators as generalizations of partial differential operators msc Hijazi aut Milhorat aut Moroianu aut Moroianu aut https://ems.press/doi/10.4171/136 cover image https://content.ems.press/assets/public/images/books/cover-216.jpg nam a22 5a 4500 10.4171/154 DE-4084 2015-08-20 a fot 00| 0| cr nn mmmmamaa 150820e20150820gw fot 00| 0|eng d 9783037196540 10.4171/154 doi DE-4084 PB bicssc 57M05 msc 20E26 msc Aschenbrenner aut 3-Manifold Groups. EMS Press 2015 1 online resource (230 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 20 2523-5184 Restricted to subscribers. https://ems.press/books The field of 3-manifold topology has made great strides forward since 1982, when Thurston articulated his influential list of questions. Primary among these is Perelman's proof of the Geometrization Conjecture, but other highlights include the Tameness Theorem of Agol and Calegari-Gabai, the Surface Subgroup Theorem of Kahn-Markovic, the work of Wise and others on special cube complexes, and finally Agol's proof of the Virtual Haken Conjecture. This book summarizes all these developments and provides an exhaustive account of the current state of the art of 3-manifold topology, especially focussing on the consequences for fundamental groups of 3-manifolds. As the first book on 3-manifold topology that incorporates the exciting progress of the last two decades, it will be an invaluable resource for researchers in the field who need a reference for these developments. It also gives a fast-paced introduction to this material - although some familiarity with the fundamental group is recommended, little other previous knowledge is assumed, and the book is accessible to graduate students. The book closes with an extensive list of open questions, which will also be of interest to graduate students and established researchers alike. Mathematics bicssc Fundamental group, presentations, free differential calculus msc Residual properties and generalizations; residually finite groups msc Friedl aut Wilton aut https://ems.press/doi/10.4171/154 cover image https://content.ems.press/assets/public/images/books/cover-217.jpg nam a22 5a 4500 10.4171/155 DE-4084 2015-09-30 a fot 00| 0| cr nn mmmmamaa 150930e20150930gw fot 00| 0|eng d 9783037196557 10.4171/155 doi DE-4084 PB bicssc 46-XX msc 42-XX msc Triebel aut Tempered Homogeneous Function Spaces. EMS Press 2015 1 online resource (143 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 21 2523-5184 Restricted to subscribers. https://ems.press/books If one tries to transfer assertions for the inhomogeneous spaces A^s_{p,q} (\mathbb R^n), A \in \{B,F \}, appropriately to their homogeneous counterparts {\overset {\, \ast}{A}}{}^s_{p,q} (\mathbb R^n) within the framework of the dual pairing \big( S(\mathbb R^n), S'(\mathbb R^n) \big) then it is hard to make a mistake as long as the parameters p,q,s are restricted by 0 < p,q \le \infty and, in particular, n(\frac {1}{p} - 1) < s < \frac {n}{p}. It is the main aim of these notes to say what this means. This book is addressed to graduate students and mathematicians having a working knowledge of basic elements of the theory of function spaces, especially of type B^s_{p,q} and F^s_{p,q}. Mathematics bicssc Functional analysis msc Harmonic analysis on Euclidean spaces msc https://ems.press/doi/10.4171/155 cover image https://content.ems.press/assets/public/images/books/cover-218.jpg nam a22 5a 4500 10.4171/142 DE-4084 2015-11-23 a fot 00| 0| cr nn mmmmamaa 151123e20151123gw fot 00| 0|eng d 9783037196427 10.4171/142 doi DE-4084 PB bicssc 11-02 msc 11J81 msc 11A63 msc 11J04 msc 11J13 msc 11J68 msc 11J70 msc 11J87 msc 68R15 msc Bringmann aut Four Faces of Number Theory. EMS Press 2015 1 online resource (198 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 22 2523-5184 Restricted to subscribers. https://ems.press/books This book arose from courses given at the International Summer School organized in August 2012 by the number theory group of the Department of Mathematics at the University of Würzburg. It consists of four essentially self-contained chapters and presents recent research results highlighting the strong interplay between number theory and other fields of mathematics, such as combinatorics, functional analysis and graph theory. The book is addressed to (under)graduate students who wish to discover various aspects of number theory. Remarkably, it demonstrates how easily one can approach frontiers of current research in number theory by elementary and basic analytic methods. Kathrin Bringmann gives an introduction to the theory of modular forms and, in particular, so-called Mock theta-functions, a topic which had been untouched for decades but has obtained much attention in the last years. Yann Bugeaud is concerned with expansions of algebraic numbers. Here combinatorics on words and transcendence theory are combined to derive new information on the sequence of decimals of algebraic numbers and on their continued fraction expansions. Titus Hilberdink reports on a recent and rather unexpected approach to extreme values of the Riemann zeta-function by use of (multiplicative) Toeplitz matrices and functional analysis. Finally, Jürgen Sander gives an introduction to algebraic graph theory and the impact of number theoretical methods on fundamental questions about the spectra of graphs and the analogue of the Riemann hypothesis. Mathematics bicssc Research exposition (monographs, survey articles) pertaining to number theory msc Transcendence (general theory) msc Radix representation; digital problems msc Homogeneous approximation to one number msc Simultaneous homogeneous approximation, linear forms msc Approximation to algebraic numbers msc Continued fractions and generalizations msc Schmidt Subspace Theorem and applications msc Combinatorics on words msc Bugeaud aut Hilberdink aut Sander aut https://ems.press/doi/10.4171/142 cover image https://content.ems.press/assets/public/images/books/cover-219.jpg nam a22 5a 4500 10.4171/145 DE-4084 2016-01-31 a fot 00| 0| cr nn mmmmamaa 160131e20160131gw fot 00| 0|eng d 9783037196458 10.4171/145 doi DE-4084 PBX bicssc 30F10 msc 01A55 msc 14H55 msc 30-01 msc 30-03 msc 30Fxx msc de Saint-Gervais aut Uniformization of Riemann Surfaces ; Revisiting a hundred-year-old theorem. EMS Press 2016 1 online resource (512 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 11 2523-5222 Restricted to subscribers. https://ems.press/books In 1907 Paul Koebe and Henri Poincaré almost simultaneously proved the uniformization theorem: _Every simply connected Riemann surface is isomorphic to the plane, the open unit disc, or the sphere._ It took a whole century to get to the point of stating this theorem and providing a convincing proof of it, relying as it did on prior work of Gauss, Riemann, Schwarz, Klein, Poincaré, and Koebe, among others. The present book offers an overview of the maturation process of this theorem. The evolution of the uniformization theorem took place in parallel with the emergence of modern algebraic geometry, the creation of complex analysis, the first stirrings of functional analysis, and with the flowering of the theory of differential equations and the birth of topology. The uniformization theorem was thus one of the lightning rods of 19th century mathematics. Rather than describe the history of a single theorem, our aim is to return to the original proofs, to look at these through the eyes of modern mathematicians, to enquire as to their correctness, and to attempt to make them rigorous while respecting insofar as possible the state of mathematical knowledge at the time, or, if this should prove impossible, then using modern mathematical tools not available to their authors. This book will be useful to today's mathematicians wishing to cast a glance back at the history of their discipline. It should also provide graduate students with a non-standard approach to concepts of great importance for modern research. Translated from the French by Robert G. Burns. History of mathematics bicssc Compact Riemann surfaces and uniformization msc History of mathematics in the 19th century msc Riemann surfaces; Weierstrass points; gap sequences msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable msc History of functions of a complex variable msc Riemann surfaces msc https://ems.press/doi/10.4171/145 cover image https://content.ems.press/assets/public/images/books/cover-222.jpg nam a22 5a 4500 10.4171/158 DE-4084 2016-01-05 a fot 00| 0| cr nn mmmmamaa 160105e20160105gw fot 00| 0|eng d 9783037196588 10.4171/158 doi DE-4084 PBMP bicssc PBT bicssc 53C23 msc 28A33 msc 30Lxx msc 35P15 msc 53C20 msc 54Exx msc 58C40 msc 58J50 msc 60B10 msc Shioya aut Metric Measure Geometry ; Gromovs Theory of Convergence and Concentration of Metrics and Measures. EMS Press 2016 1 online resource (194 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 25 2523-5141 Restricted to subscribers. https://ems.press/books This book studies a new theory of metric geometry on metric measure spaces, originally developed by M. Gromov in his book Metric Structures for Riemannian and Non-Riemannian Spaces and based on the idea of the concentration of measure phenomenon due to Lévy and Milman. A central theme in this text is the study of the observable distance between metric measure spaces, defined by the difference between 1-Lipschitz functions on one space and those on the other. The topology on the set of metric measure spaces induced by the observable distance function is weaker than the measured Gromov-Hausdorff topology and allows to investigate a sequence of Riemannian manifolds with unbounded dimensions. One of the main parts of this presentation is the discussion of a natural compactification of the completion of the space of metric measure spaces. The stability of the curvature-dimension condition is also discussed. This book makes advanced material accessible to researchers and graduate students interested in metric measure spaces. Differential & Riemannian geometry bicssc Probability & statistics bicssc Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces msc Spaces of measures, convergence of measures msc Analysis on metric spaces msc Estimates of eigenvalues in context of PDEs msc Global Riemannian geometry, including pinching msc Topological spaces with richer structures msc Spectral theory; eigenvalue problems on manifolds msc Spectral problems; spectral geometry; scattering theory on manifolds msc Convergence of probability measures msc https://ems.press/doi/10.4171/158 cover image https://content.ems.press/assets/public/images/books/cover-220.jpg nam a22 5a 4500 10.4171/160 DE-4084 2016-01-11 a fot 00| 0| cr nn mmmmamaa 160111e20160111gw fot 00| 0|eng d 9783037196601 10.4171/160 doi DE-4084 PB bicssc 30-00 msc 32-00 msc 57-00 msc 32G13 msc 32G15 msc 30F60 msc 11F06 msc 11F75 msc 14D20 msc 14H15 msc 14H60 msc 14H55 msc 14J60 msc 20F14 msc 20F28 msc 20F38 msc 20F65 msc 20F67 msc 20H10 msc 22E46 msc 30-03 msc 30C62 msc 30F20 msc 30F25 msc 30F10 msc 30F15 msc 30F30 msc 30F35 msc 30F40 msc 30F45 msc 32-03 msc 32S30 msc 53A35 msc 53B35 msc 53C35 msc 53C50 msc 53C80 msc 53D55 msc 53Z05 msc 57M07 msc 57M50 msc 57M60 msc 57N16 msc Papadopoulos edt Handbook of Teichmüller Theory, Volume V. EMS Press 2016 1 online resource (596 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 26 2523-5141 Restricted to subscribers. https://ems.press/books This volume is the fifth in a series dedicated to Teichmüller theory in a broad sense, including the study of various deformation spaces and of mapping class group actions. It is divided into four parts: Part A: The metric and the analytic theory Part B: The group theory Part C: Representation theory and generalized structures Part D: Sources The topics that are covered include identities for the hyperbolic geodesic length spectrum, Thurston's metric, the cohomology of moduli space and mapping class groups, the Johnson homomorphisms, Higgs bundles, dynamics on character varieties, and there are many others. Besides surveying important parts of the theory, several chapters contain conjectures and open problems. The last part contains two fundamental papers by Teichmüller, translated into English and accompanied by mathematical commentaries. The chapters, like those of the other volumes in this collection, are written by experts who have a broad view on the subject. They have an expository character (which fits with the original purpose of this handbook), but some of them also contain original and new material. The Handbook is addressed to researchers and to graduate students. Mathematics bicssc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functions of a complex variable msc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to several complex variables and analytic spaces msc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to manifolds and cell complexes msc Complex-analytic moduli problems msc Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) msc Teichmüller theory for Riemann surfaces msc Structure of modular groups and generalizations; arithmetic groups msc Cohomology of arithmetic groups msc Algebraic moduli problems, moduli of vector bundles msc Families, moduli of curves (analytic) msc Vector bundles on curves and their moduli msc Riemann surfaces; Weierstrass points; gap sequences msc Vector bundles on surfaces and higher-dimensional varieties, and their moduli msc Derived series, central series, and generalizations for groups msc Automorphism groups of groups msc Other groups related to topology or analysis msc Geometric group theory msc Hyperbolic groups and nonpositively curved groups msc Fuchsian groups and their generalizations (group-theoretic aspects) msc Semisimple Lie groups and their representations msc History of functions of a complex variable msc Quasiconformal mappings in the complex plane msc Classification theory of Riemann surfaces msc Ideal boundary theory for Riemann surfaces msc Compact Riemann surfaces and uniformization msc Harmonic functions on Riemann surfaces msc Differentials on Riemann surfaces msc Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) msc Kleinian groups (aspects of compact Riemann surfaces and uniformization) msc Conformal metrics (hyperbolic, Poincaré, distance functions) msc History of several complex variables and analytic spaces msc Deformations of complex singularities; vanishing cycles msc Non-Euclidean differential geometry msc Local differential geometry of Hermitian and Kählerian structures msc Differential geometry of symmetric spaces msc Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics msc Applications of global differential geometry to the sciences msc Deformation quantization, star products msc Applications of differential geometry to physics msc Topological methods in group theory msc General geometric structures on low-dimensional manifolds msc Group actions on manifolds and cell complexes in low dimensions msc Geometric structures on manifolds of high or arbitrary dimension msc https://ems.press/doi/10.4171/160 cover image https://content.ems.press/assets/public/images/books/cover-221.jpg nam a22 5a 4500 10.4171/159 DE-4084 2016-03-29 a fot 00| 0| cr nn mmmmamaa 160329e20160329gw fot 00| 0|eng d 9783037196595 10.4171/159 doi DE-4084 PBKB bicssc 28-01 msc 28C05 msc 28C10 msc 28C15 msc 35J05 msc 43A05 msc 44A35 msc 46B22 msc 46C05 msc 46E27 msc 46E30 msc Salamon aut Measure and Integration. EMS Press 2016 1 online resource (363 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 17 2943-4955 Restricted to subscribers. https://ems.press/books The book is intended as a companion to a one semester introductory lecture course on measure and integration. After an introduction to abstract measure theory it proceeds to the construction of the Lebesgue measure and of Borel measures on locally compact Hausdorff spaces, L^p spaces and their dual spaces and elementary Hilbert space theory. Special features include the formulation of the Riesz Representation Theorem in terms of both inner and outer regularity, the proofs of the Marcinkiewicz Interpolation Theorem and the Calderon-Zygmund inequality as applications of Fubinis theorem and Lebesgue differentiation, the treatment of the generalized Radon-Nikodym theorem due to Fremlin, and the existence proof for Haar measures. Three appendices deal with Urysohns Lemma, product topologies, and the inverse function theorem. The book assumes familiarity with first year analysis and linear algebra. It is suitable for second year undergraduate students of mathematics or anyone desiring an introduction to the concepts of measure and integration. Real analysis, real variables bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration msc Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures msc Set functions and measures on topological groups or semigroups, Haar measures, invariant measures msc Set functions and measures on topological spaces (regularity of measures, etc.) msc Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation msc Measures on groups and semigroups, etc. msc Convolution as an integral transform msc Radon-Nikodým, Kreĭn-Milman and related properties msc Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) msc Spaces of measures msc Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) msc https://ems.press/doi/10.4171/159 cover image https://content.ems.press/assets/public/images/books/cover-128.jpg nam a22 5a 4500 10.4171/161 DE-4084 2016-05-31 a fot 00| 0| cr nn mmmmamaa 160531e20160531gw fot 00| 0|eng d 9783037196618 10.4171/161 doi DE-4084 PB bicssc 30-00 msc 32-00 msc 57-00 msc 32G13 msc 32G15 msc 30F60 msc 11F06 msc 11F75 msc 14D20 msc 11G32 msc 14C05 msc 14H15 msc 14H30 msc 14H60 msc 14H55 msc 14J60 msc 18A22 msc 20F14 msc 20F28 msc 20F38 msc 20F65 msc 20F67 msc 20H10 msc 22E46 msc 30-03 msc 30C62 msc 30F20 msc 30F25 msc 30F10 msc 30F15 msc 30F30 msc 30F35 msc 30F40 msc 30F45 msc 32-03 msc 32S30 msc 53A35 msc 53B35 msc 53C35 msc 53C50 msc 53C80 msc 53D55 msc 53Z05 msc 57M07 msc 57M50 msc 57M60 msc 57N16 msc Papadopoulos edt Handbook of Teichmüller Theory, Volume VI. EMS Press 2016 1 online resource (652 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 27 2523-5141 Restricted to subscribers. https://ems.press/books This volume is the sixth in a series dedicated to Teichmüller theory in a broad sense, including various moduli and deformation spaces, and the study of mapping class groups. It is divided into five parts: Part A: The metric and the analytic theory. Part B: The group theory. Part C: Representation theory and generalized structures. Part D: The Grothendieck-Teichmüller theory. Part D: Sources. The topics surveyed include Grothendiecks construction of the analytic structure of Teichmüller space, identities on the geodesic length spectrum of hyperbolic surfaces (including Mirzakhanis application to the computation of Weil-Petersson volumes), moduli spaces of configurations spaces, the Teichmüller tower with the action of the Galois group on dessins denfants, and several others actions related to surfaces. The last part contains three papers by Teichmüller, translated into English with mathematical commentaries, and a document that contains H. Grötzschs comments on Teichmüllers famous paper _Extremale quasikonforme Abbildungen und quadratische Differentiale_. The handbook is addressed to researchers and to graduate students. Mathematics bicssc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functions of a complex variable msc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to several complex variables and analytic spaces msc General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to manifolds and cell complexes msc Complex-analytic moduli problems msc Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) msc Teichmüller theory for Riemann surfaces msc Structure of modular groups and generalizations; arithmetic groups msc Cohomology of arithmetic groups msc Algebraic moduli problems, moduli of vector bundles msc Arithmetic aspects of dessins d'enfants, Belyĭ theory msc Parametrization (Chow and Hilbert schemes) msc Families, moduli of curves (analytic) msc Coverings of curves, fundamental group msc Vector bundles on curves and their moduli msc Riemann surfaces; Weierstrass points; gap sequences msc Vector bundles on surfaces and higher-dimensional varieties, and their moduli msc Special properties of functors (faithful, full, etc.) msc Derived series, central series, and generalizations for groups msc Automorphism groups of groups msc Other groups related to topology or analysis msc Geometric group theory msc Hyperbolic groups and nonpositively curved groups msc Fuchsian groups and their generalizations (group-theoretic aspects) msc Semisimple Lie groups and their representations msc History of functions of a complex variable msc Quasiconformal mappings in the complex plane msc Classification theory of Riemann surfaces msc Ideal boundary theory for Riemann surfaces msc Compact Riemann surfaces and uniformization msc Harmonic functions on Riemann surfaces msc Differentials on Riemann surfaces msc Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) msc Kleinian groups (aspects of compact Riemann surfaces and uniformization) msc Conformal metrics (hyperbolic, Poincaré, distance functions) msc History of several complex variables and analytic spaces msc Deformations of complex singularities; vanishing cycles msc Non-Euclidean differential geometry msc Local differential geometry of Hermitian and Kählerian structures msc Differential geometry of symmetric spaces msc Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics msc Applications of global differential geometry to the sciences msc Deformation quantization, star products msc Applications of differential geometry to physics msc Topological methods in group theory msc General geometric structures on low-dimensional manifolds msc Group actions on manifolds and cell complexes in low dimensions msc Geometric structures on manifolds of high or arbitrary dimension msc https://ems.press/doi/10.4171/161 cover image https://content.ems.press/assets/public/images/books/cover-129.jpg nam a22 5a 4500 10.4171/156 DE-4084 2016-05-31 a fot 00| 0| cr nn mmmmamaa 160531e20160531gw fot 00| 0|eng d 9783037196564 10.4171/156 doi DE-4084 PBP bicssc 57P05 msc 57P10 msc 57P99 msc 57R65 msc 57R67 msc 18F15 msc 19J25 msc 57N60 msc 57N65 msc Cavicchioli aut Higher-Dimensional Generalized Manifolds: Surgery and Constructions. EMS Press 2016 1 online resource (154 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 23 2523-5184 Restricted to subscribers. https://ems.press/books Generalized manifolds are a most fascinating subject to study. They were introduced in the 1930s, when topologists tried to detect topological manifolds among more general spaces (this is nowadays called the manifold recognition problem). As such, generalized manifolds have served to understand the nature of genuine manifolds. However, it soon became more important to study the category of generalized manifolds itself. A breakthrough was made in the 1990s, when several topologists discovered a systematic way of constructing higher-dimensional generalized manifolds, based on advanced surgery techniques. In fact, the development of controlled surgery theory and the study of generalized manifolds developed in parallel. In this process, earlier studies of geometric surgery turned out to be very helpful. Generalized manifolds will continue to be an attractive subject to study, for there remain several unsolved fundamental problems. Moreover, they hold promise for new research, e.g. for finding appropriate structures on these spaces which could bring to light geometric (or even analytic) aspects of higher-dimensional generalized manifolds. This is the first book to systematically collectthe most important material on higher-dimensional generalized manifolds and controlled surgery. It is self-contained and its extensive list of references reflects the historic development. The book is based on our graduate courses and seminars, as well as our talks given at various meetings, and is suitable for advanced graduate students and researchers in algebraic and geometric topology. Topology bicssc Local properties of generalized manifolds msc Poincaré duality spaces msc Generalized manifolds msc Surgery and handlebodies msc Surgery obstructions, Wall groups msc Abstract manifolds and fiber bundles (category-theoretic aspects) msc Surgery obstructions (\(K\)-theoretic aspects) msc Cellularity in topological manifolds msc Algebraic topology of manifolds msc Hegenbarth aut Repovš aut https://ems.press/doi/10.4171/156 cover image https://content.ems.press/assets/public/images/books/cover-137.jpg nam a22 5a 4500 10.4171/157 DE-4084 2016-07-25 a fot 00| 0| cr nn mmmmamaa 160725e20160725gw fot 00| 0|eng d 9783037196571 10.4171/157 doi DE-4084 PBV bicssc 05E18 msc 11M26 msc 13F35 msc 14A15 msc 14A20 msc 14A22 msc 14G15 msc 14G40 msc 14H10 msc 18A05 msc 19E08 msc 20B25 msc 20G05 msc 20G35 msc 20M25 msc 51E24 msc 05E05 msc 06B10 msc 11G20 msc 11G25 msc 11R18 msc 11T55 msc 13A35 msc 13C60 msc 14C40 msc 14L15 msc 14M25 msc 14P10 msc 15B48 msc 16G20 msc 16Y60 msc 18F20 msc 20E42 msc 20F36 msc 20M14 msc 20M32 msc 20N20 msc 51B25 msc 55N30 msc 55P42 msc 55Q45 msc Thas edt Absolute Arithmetic and -Geometry. EMS Press 2016 1 online resource (397 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books It has been known for some time that geometries over finite fields, their automorphism groups and certain counting formulae involving these geometries have interesting guises when one lets the size of the field go to 1. On the other hand, the nonexistent field with one element, \mathbb F_1, presents itself as a ghost candidate for an absolute basis in Algebraic Geometry to perform the Deninger-Manin program, which aims at solving the classical Riemann Hypothesis. This book, which is the first of its kind in the \mathbb F_1\-world, covers several areas in \mathbb F_1\-theory, and is divided into four main parts - Combinatorial Theory, Homological Algebra, Algebraic Geometry and Absolute Arithmetic. Topics treated include the combinatorial theory and geometry behind \mathbb F_1, categorical foundations, the blend of different scheme theories over \mathbb F_1 which are presently available, motives and zeta functions, the Habiro topology, Witt vectors and total positivity, moduli operads, and at the end, even some arithmetic. Each chapter is carefully written by experts, and besides elaborating on known results, brand new results, open problems and conjectures are also met along the way. The diversity of the contents, together with the mystery surrounding the field with one element, should attract any mathematician, regardless of speciality. Combinatorics & graph theory bicssc Group actions on combinatorial structures msc Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses msc Witt vectors and related rings msc Schemes and morphisms msc Generalizations (algebraic spaces, stacks) msc Noncommutative algebraic geometry msc Finite ground fields in algebraic geometry msc Arithmetic varieties and schemes; Arakelov theory; heights msc Families, moduli of curves (algebraic) msc Definitions and generalizations in theory of categories msc \(K\)-theory of schemes msc Finite automorphism groups of algebraic, geometric, or combinatorial structures msc Representation theory for linear algebraic groups msc Linear algebraic groups over adèles and other rings and schemes msc Semigroup rings, multiplicative semigroups of rings msc Buildings and the geometry of diagrams msc Symmetric functions and generalizations msc Lattice ideals, congruence relations msc Curves over finite and local fields msc Varieties over finite and local fields msc Cyclotomic extensions msc Arithmetic theory of polynomial rings over finite fields msc Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure msc Module categories and commutative rings msc Riemann-Roch theorems msc Group schemes msc Toric varieties, Newton polyhedra, Okounkov bodies msc Semialgebraic sets and related spaces msc Positive matrices and their generalizations; cones of matrices msc Representations of quivers and partially ordered sets msc Semirings msc Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) msc Groups with a \(BN\)-pair; buildings msc Braid groups; Artin groups msc Commutative semigroups msc Algebraic monoids msc Hypergroups msc Lie geometries in nonlinear incidence geometry msc Sheaf cohomology in algebraic topology msc Stable homotopy theory, spectra msc Stable homotopy of spheres msc https://ems.press/doi/10.4171/157 cover image https://content.ems.press/assets/public/images/books/cover-135.jpg nam a22 5a 4500 10.4171/162 DE-4084 2016-06-30 a fot 00| 0| cr nn mmmmamaa 160630e20160630gw fot 00| 0|eng d 9783037196625 10.4171/162 doi DE-4084 PBMP bicssc 53C17 msc 35H10 msc 60H30 msc 49J15 msc Barilari edt Geometry, Analysis and Dynamics on sub-Riemannian Manifolds. Volume I EMS Press 2016 1 online resource (332 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 24 2523-5184 Restricted to subscribers. https://ems.press/books Sub-Riemannian manifolds model media with constrained dynamics: motion at any point is only allowed along a limited set of directions, which are prescribed by the physical problem. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators and degenerate diffusions on manifolds. In the last twenty years, sub-Riemannian geometry has emerged as an independent research domain, with extremely rich motivations and ramifications in several parts of pure and applied mathematics, such as geometric analysis, geometric measure theory, stochastic calculus and evolution equations together with applications in mechanics, optimal control and biology. The aim of the lectures collected here is to present sub-Riemannian structures for the use of both researchers and graduate students. Differential & Riemannian geometry bicssc Sub-Riemannian geometry msc Hypoelliptic equations msc Applications of stochastic analysis (to PDEs, etc.) msc Existence theories for optimal control problems involving ordinary differential equations msc Boscain edt Sigalotti edt https://ems.press/doi/10.4171/162 cover image https://content.ems.press/assets/public/images/books/cover-130.jpg nam a22 5a 4500 10.4171/163 DE-4084 2016-10-25 a fot 00| 0| cr nn mmmmamaa 161025e20161025gw fot 00| 0|eng d 9783037196632 10.4171/163 doi DE-4084 PBMP bicssc 53C17 msc 35H10 msc 60H30 msc 49J15 msc Barilari edt Geometry, Analysis and Dynamics on sub-Riemannian Manifolds. Volume II EMS Press 2016 1 online resource (307 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 25 2523-5184 Restricted to subscribers. https://ems.press/books Sub-Riemannian manifolds model media with constrained dynamics: motion at any point is only allowed along a limited set of directions, which are prescribed by the physical problem. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators and degenerate diffusions on manifolds. In the last twenty years, sub-Riemannian geometry has emerged as an independent research domain, with extremely rich motivations and ramifications in several parts of pure and applied mathematics, such as geometric analysis, geometric measure theory, stochastic calculus and evolution equations together with applications in mechanics, optimal control and biology. The aim of the lectures collected here is to present sub-Riemannian structures for the use of both researchers and graduate students. Differential & Riemannian geometry bicssc Sub-Riemannian geometry msc Hypoelliptic equations msc Applications of stochastic analysis (to PDEs, etc.) msc Existence theories for optimal control problems involving ordinary differential equations msc Boscain edt Sigalotti edt https://ems.press/doi/10.4171/163 cover image https://content.ems.press/assets/public/images/books/cover-138.jpg nam a22 5a 4500 10.4171/164 DE-4084 2016-07-04 a fot 00| 0| cr nn mmmmamaa 160704e20160704gw fot 00| 0|eng d 9783037196649 10.4171/164 doi DE-4084 PB bicssc 00-XX msc König edt Mathematics and Society. EMS Press 2016 1 online resource (314 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books The ubiquity and importance of mathematics in our complex society is generally not in doubt. However, even a scientifically interested layman would be hard pressed to point out aspects of our society where contemporary mathematical research is essential. Most popular examples are finance, engineering, wheather and industry, but the way mathematics comes into play is widely unknown in the public. And who thinks of application fields like biology, encryption, architecture, or voting systems? This volume comprises a number of success stories of mathematics in our society - important areas being shaped by cutting edge mathematical research. The authors are eminent mathematicians with a high sense for public presentation, addressing scientifically interested laymen as well as professionals in mathematics and its application disciplines. Mathematics bicssc General and overarching topics; collections msc https://ems.press/doi/10.4171/164 cover image https://content.ems.press/assets/public/images/books/cover-132.jpg nam a22 5a 4500 10.4171/165 DE-4084 2016-07-31 a fot 00| 0| cr nn mmmmamaa 160731e20160731gw fot 00| 0|eng d 9783037196656 10.4171/165 doi DE-4084 PB bicssc 46L54 msc 60B20 msc 47C15 msc 20G42 msc Voiculescu edt Free Probability and Operator Algebras. EMS Press 2016 1 online resource (142 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Münster Lectures in Mathematics (mlm) 1 2523-5249 Restricted to subscribers. https://ems.press/books Free probability is a probability theory dealing with variables having the highest degree of noncommutativity, an aspect found in many areas (quantum mechanics, free group algebras, random matrices etc). Thirty years after its foundation, it is a well-established and very active field of mathematics. Originating from Voiculescus attempt to solve the free group factor problem in operator algebras, free probability has important connections with random matrix theory, combinatorics, harmonic analysis, representation theory of large groups, and wireless communication. These lecture notes arose from a masterclass in Münster, Germany and present the state of free probability from an operator algebraic perspective. This volume includes introductory lectures on random matrices and combinatorics of free probability (Speicher), free monotone transport (Shlyakhtenko), free group factors (Dykema), free convolution (Bercovici), easy quantum groups (Weber), and a historical review with an outlook (Voiculescu). In order to make it more accessible, the exposition features a chapter on basics in free probability, and exercises for each part. This book is aimed at master students to early career researchers familiar with basic notions and concepts from operator algebras. Mathematics bicssc Free probability and free operator algebras msc Random matrices (probabilistic aspects) msc Linear operators in \(C^*\)- or von Neumann algebras msc Quantum groups (quantized function algebras) and their representations msc Stammeier edt Weber edt https://ems.press/doi/10.4171/165 cover image https://content.ems.press/assets/public/images/books/cover-133.jpg nam a22 5a 4500 10.4171/166 DE-4084 2016-09-30 a fot 00| 0| cr nn mmmmamaa 160930e20160930gw fot 00| 0|eng d 9783037196663 10.4171/166 doi DE-4084 PB bicssc 20F65 msc 20F05 msc 22D05 msc 51F99 msc 54E35 msc 57M07 msc 57T20 msc Cornulier aut Metric Geometry of Locally Compact Groups. EMS Press 2016 1 online resource (243 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 25 2943-5005 Restricted to subscribers. https://ems.press/books **Winner of the 2016 EMS Monograph Award** The main aim of this book is the study of locally compact groups from a geometric perspective, with an emphasis on appropriate metrics that can be defined on them. The approach has been successful for finitely generated groups, and can favourably be extended to locally compact groups. Parts of the book address the coarse geometry of metric spaces, where coarse refers to that part of geometry concerning properties that can be formulated in terms of large distances only. This point of view is instrumental in studying locally compact groups. Basic results in the subject are exposed with complete proofs, others are stated with appropriate references. Most importantly, the development of the theory is illustrated by numerous examples, including matrix groups with entries in the the field of real or complex numbers, or other locally compact fields such as p-adic fields, isometry groups of various metric spaces, and, last but not least, discrete group themselves. The book is aimed at graduate students and advanced undergraduate students, as well as mathematicians who wish some introduction to coarse geometry and locally compact groups. Mathematics bicssc Geometric group theory msc Generators, relations, and presentations of groups msc General properties and structure of locally compact groups msc Metric geometry msc Metric spaces, metrizability msc Topological methods in group theory msc Homotopy groups of topological groups and homogeneous spaces msc de la Harpe aut https://ems.press/doi/10.4171/166 cover image https://content.ems.press/assets/public/images/books/cover-131.jpg nam a22 5a 4500 10.4171/167 DE-4084 2017-01-12 a fot 00| 0| cr nn mmmmamaa 170112e20170112gw fot 00| 0|eng d 9783037196670 10.4171/167 doi DE-4084 PBKD bicssc 32W20 msc 32U20 msc 32Q20 msc 35D30 msc 53C55 msc 32U15 msc 32U40 msc 35B65 msc Guedj aut Degenerate Complex Monge-Ampère Equations. EMS Press 2017 1 online resource (496 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 26 2943-5005 Restricted to subscribers. https://ems.press/books **Winner of the 2016 EMS Monograph Award** Complex Monge-Ampère equations have been one of the most powerful tools in Kähler geometry since Aubin and Yaus classical works, culminating in Yaus solution to the Calabi conjecture. A notable application is the construction of Kähler-Einstein metrics on some compact Kähler manifolds. In recent years degenerate complex Monge-Ampère equations have been intensively studied, requiring more advanced tools. The main goal of this book is to give a self-contained presentation of the recent developments of pluripotential theory on compact Kähler manifolds and its application to Kähler-Einstein metrics on mildly singular varieties. After reviewing basic properties of plurisubharmonic functions, Bedford-Taylors local theory of complex Monge-Ampère measures is developed. In order to solve degenerate complex Monge-Ampère equations on compact Kähler manifolds, fine properties of quasi-plurisubharmonic functions are explored, classes of finite energies defined and various maximum principles established. After proving Yaus celebrated theorem as well as its recent generalizations, the results are then used to solve the (singular) Calabi conjecture and to construct (singular) Kähler-Einstein metrics on some varieties with mild singularities. The book is accessible to advanced students and researchers of complex analysis and differential geometry. Complex analysis, complex variables bicssc Complex Monge-Ampère operators msc Capacity theory and generalizations msc Kähler-Einstein manifolds msc Weak solutions to PDEs msc Global differential geometry of Hermitian and Kählerian manifolds msc General pluripotential theory msc Currents msc Smoothness and regularity of solutions to PDEs msc Zeriahi aut https://ems.press/doi/10.4171/167 cover image https://content.ems.press/assets/public/images/books/cover-134.jpg nam a22 5a 4500 10.4171/168 DE-4084 2016-11-30 a fot 00| 0| cr nn mmmmamaa 161130e20161130gw fot 00| 0|eng d 9783037196687 10.4171/168 doi DE-4084 PBKJ bicssc 37Axx msc 37Bxx msc 37Dxx msc 37Fxx msc 37Hxx msc 53Axx msc DalBo edt Dynamics Done with Your Bare Hands ; Lecture notes by Diana Davis, Bryce Weaver, Roland K. W. Roeder, Pablo Lessa. EMS Press 2016 1 online resource (214 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 26 2523-5184 Restricted to subscribers. https://ems.press/books This book arose from 4 lectures given at the Undergraduate Summer School of the Thematic Program Dynamics and Boundaries held at the University of Notre Dame. It is intended to introduce (under)graduate students to the field of dynamical systems by emphasizing elementary examples, exercises and bare hands constructions. The lecture of Diana Davis is devoted to billiard flows on polygons, a simple-sounding class of continuous time dynamical system for which many problems remain open. Bryce Weaver focuses on the dynamics of a 2x2 matrix acting on the flat torus. This example introduced by Vladimir Arnold illustrates the wide class of uniformly hyperbolic dynamical systems, including the geodesic flow for negatively curved, compact manifolds. Roland Roeder considers a dynamical system on the complex plane governed by a quadratic map with a complex parameter. These maps exhibit complicated dynamics related to the Mandelbrot set defined as the set of parameters for which the orbit remains bounded. Pablo Lessa deals with a type of non-deterministic dynamical system: a simple walk on an infinite graph, obtained by starting at a vertex and choosing a random neighbor at each step. The central question concerns the recurrence property. When the graph is a Cayley graph of a group, the behavior of the walk is deeply related to algebraic properties of the group. Differential calculus & equations bicssc Ergodic theory msc Topological dynamics msc Dynamical systems with hyperbolic behavior msc Dynamical systems over complex numbers msc Random dynamical systems msc Classical differential geometry msc Ledrappier edt Wilkinson edt https://ems.press/doi/10.4171/168 cover image https://content.ems.press/assets/public/images/books/cover-136.jpg nam a22 5a 4500 10.4171/169 DE-4084 2017-01-01 a fot 00| 0| cr nn mmmmamaa 170101e20170101gw fot 00| 0|eng d 9783037196694 10.4171/169 doi DE-4084 PBKJ bicssc PBCD bicssc 35P15 msc 35P20 msc 49R05 msc 81Q10 msc 81Q20 msc Raymond aut Bound States of the Magnetic Schrödinger Operator. EMS Press 2017 1 online resource (394 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 27 2943-5005 Restricted to subscribers. https://ems.press/books This book is a synthesis of recent advances in the spectral theory of the magnetic Schrödinger operator. It can be considered a catalog of concrete examples of magnetic spectral asymptotics. Since the presentation involves many notions of spectral theory and semiclassical analysis, it begins with a concise account of concepts and methods used in the book and is illustrated by many elementary examples. Assuming various points of view (power series expansions, Feshbach-Grushin reductions, WKB constructions, coherent states decompositions, normal forms) a theory of Magnetic Harmonic Approximation is then established which allows, in particular, accurate descriptions of the magnetic eigenvalues and eigenfunctions. Some parts of this theory, such as those related to spectral reductions or waveguides, are still accessible to advanced students while others (e.g., the discussion of the Birkhoff normal form and its spectral consequences, or the results related to boundary magnetic wells in dimension three) are intended for seasoned researchers. Differential calculus & equations bicssc Mathematical logic bicssc Estimates of eigenvalues in context of PDEs msc Asymptotic distributions of eigenvalues in context of PDEs msc Variational methods for eigenvalues of operators msc Selfadjoint operator theory in quantum theory, including spectral analysis msc Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory msc https://ems.press/doi/10.4171/169 cover image https://content.ems.press/assets/public/images/books/cover-139.jpg nam a22 5a 4500 10.4171/170 DE-4084 2017-01-01 a fot 00| 0| cr nn mmmmamaa 170101e20170101gw fot 00| 0|eng d 9783037196700 10.4171/170 doi DE-4084 PBKJ bicssc PBMP bicssc 35J96 msc 35B65 msc 35J60 msc 35J66 msc 35B45 msc 35B50 msc 35J65 msc 53A15 msc 53C45 msc Figalli aut The Monge-Ampère Equation and Its Applications. EMS Press 2017 1 online resource (210 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 22 2943-4971 Restricted to subscribers. https://ems.press/books The Monge-Ampère equation is one of the most important partial differential equations, appearing in many problems in analysis and geometry. This monograph is a comprehensive introduction to the existence and regularity theory of the Monge-Ampère equation and some selected applications; the main goal is to provide the reader with a wealth of results and techniques he or she can draw from to understand current research related to this beautiful equation. The presentation is essentially self-contained, with an appendix wherein one can find precise statements of all the results used from different areas (linear algebra, convex geometry, measure theory, nonlinear analysis, and PDEs). This book is intended for graduate students and researchers interested in nonlinear PDEs: explanatory figures, detailed proofs, and heuristic arguments make this book suitable for self-study and also as a reference. Differential calculus & equations bicssc Differential & Riemannian geometry bicssc Monge-Ampère equations msc Smoothness and regularity of solutions to PDEs msc Nonlinear elliptic equations msc Nonlinear boundary value problems for nonlinear elliptic equations msc A priori estimates in context of PDEs msc Maximum principles in context of PDEs msc Nonlinear boundary value problems for linear elliptic equations msc Affine differential geometry msc Global surface theory (convex surfaces à la A. D. Aleksandrov) msc https://ems.press/doi/10.4171/170 cover image https://content.ems.press/assets/public/images/books/cover-140.jpg nam a22 5a 4500 10.4171/140 DE-4084 2016-10-14 a fot 00| 0| cr nn mmmmamaa 161014e20161014gw fot 00| 0|eng d 9783037196403 10.4171/140 doi DE-4084 PBK bicssc 28-02 msc 31-01 msc 35-02 msc 35R06 msc 26B20 msc 26B35 msc 26D10 msc 28A12 msc 28A25 msc 28A33 msc 28A78 msc 28C05 msc 31B05 msc 31B10 msc 31B15 msc 31B20 msc 31B35 msc 35A01 msc 35A02 msc 35A08 msc 35A15 msc 35A23 msc 35A35 msc 35B05 msc 35B33 msc 35B45 msc 35B50 msc 35B51 msc 35B60 msc 35B65 msc 35C15 msc 35D30 msc 35J05 msc 35J10 msc 35J15 msc 35J20 msc 35J25 msc 35J60 msc 35J61 msc 35J86 msc 35J91 msc 35Q40 msc 35Q75 msc 35R05 msc 46E27 msc 46E30 msc 46E35 msc 49J40 msc 49J45 msc 46N20 msc 49S05 msc Ponce aut Elliptic PDEs, Measures and Capacities ; From the Poisson Equation to Nonlinear Thomas-Fermi Problems. EMS Press 2016 1 online resource (463 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 23 2943-5005 Restricted to subscribers. https://ems.press/books **Winner of the 2014 EMS Monograph Award** Partial differential equations (PDEs) and geometric measure theory (GMT) are branches of analysis whose connections are usually not emphasized in introductory graduate courses. Yet, one cannot dissociate the notions of mass or electric charge, naturally described in terms of measures, from the physical potential they generate. Having such a principle in mind, this book illustrates the beautiful interplay between tools from PDEs and GMT in a simple and elegant way by investigating properties like existence and regularity of solutions of linear and nonlinear elliptic PDEs. Inspired by a variety of sources, from the pioneer balayage scheme of Poincaré to more recent results related to the Thomas-Fermi and the Chern-Simons models, the problems covered in this book follow an original presentation, intended to emphasize the main ideas in the proofs. Classical techniques like regularity theory, maximum principles and the method of sub- and supersolutions are adapted to the setting where merely integrability or density assumptions on the data are available. The distinguished role played by capacities and precise representatives is also explained. Other special features are: the remarkable equivalence between Sobolev capacities and Hausdorff contents in terms of trace inequalities; the strong approximation of measures in terms of capacities or densities, normally absent from GMT books; the rescue of the strong maximum principle for the Schrödinger operator involving singular potentials. This book invites the reader to a trip through modern techniques in the frontier of elliptic PDEs and GMT, and is addressed to graduate students and researchers having some deep interest in analysis. Most of the chapters can be read independently, and only basic knowledge of measure theory, functional analysis and Sobolev spaces is required. Calculus & mathematical analysis bicssc Research exposition (monographs, survey articles) pertaining to measure and integration msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to potential theory msc Research exposition (monographs, survey articles) pertaining to partial differential equations msc PDEs with measure msc Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) msc Special properties of functions of several variables, Hölder conditions, etc. msc Inequalities involving derivatives and differential and integral operators msc Contents, measures, outer measures, capacities msc Integration with respect to measures and other set functions msc Spaces of measures, convergence of measures msc Hausdorff and packing measures msc Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures msc Harmonic, subharmonic, superharmonic functions in higher dimensions msc Integral representations, integral operators, integral equations methods in higher dimensions msc Potentials and capacities, extremal length and related notions in higher dimensions msc Boundary value and inverse problems for harmonic functions in higher dimensions msc Connections of harmonic functions with differential equations in higher dimensions msc Existence problems for PDEs: global existence, local existence, non-existence msc Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness msc Fundamental solutions to PDEs msc Variational methods applied to PDEs msc Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals msc Theoretical approximation in context of PDEs msc Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs msc Critical exponents in context of PDEs msc A priori estimates in context of PDEs msc Maximum principles in context of PDEs msc Comparison principles in context of PDEs msc Continuation and prolongation of solutions to PDEs msc Smoothness and regularity of solutions to PDEs msc Integral representations of solutions to PDEs msc Weak solutions to PDEs msc Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation msc Schrödinger operator, Schrödinger equation msc Second-order elliptic equations msc Variational methods for second-order elliptic equations msc Boundary value problems for second-order elliptic equations msc Nonlinear elliptic equations msc Semilinear elliptic equations msc Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators msc Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian msc PDEs in connection with quantum mechanics msc PDEs in connection with relativity and gravitational theory msc PDEs with low regular coefficients and/or low regular data msc Spaces of measures msc Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) msc Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems msc Variational inequalities msc Methods involving semicontinuity and convergence; relaxation msc Applications of functional analysis to differential and integral equations msc Variational principles of physics msc https://ems.press/doi/10.4171/140 cover image https://content.ems.press/assets/public/images/books/cover-141.jpg nam a22 5a 4500 10.4171/173 DE-4084 2017-03-10 a fot 00| 0| cr nn mmmmamaa 170310e20170310gw fot 00| 0|eng d 9783037196731 10.4171/173 doi DE-4084 PBT bicssc 62P05 msc 91G10 msc 60G44 msc Schachermayer aut Asymptotic Theory of Transaction Costs. EMS Press 2017 1 online resource (160 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 23 2943-4971 Restricted to subscribers. https://ems.press/books A classical topic in Mathematical Finance is the theory of portfolio optimization. Robert Merton's work from the early seventies had enormous impact on academic research as well as on the paradigms guiding practitioners. One of the ramifications of this topic is the analysis of (small) proportional transaction costs, such as a Tobin tax. The lecture notes present some striking recent results of the asymptotic dependence of the relevant quantities when transaction costs tend to zero. An appealing feature of the consideration of transaction costs is that it allows for the first time to reconcile the no arbitrage paradigm with the use of non-semimartingale models, such as fractional Brownian motion. This leads to the culminating theorem of the present lectures which roughly reads as follows: for a fractional Brownian motion stock price model we always find a shadow price process for given transaction costs. This process is a semimartingale and can therefore be dealt with using the usual machinery of mathematical finance. Probability & statistics bicssc Applications of statistics to actuarial sciences and financial mathematics msc Portfolio theory msc Martingales with continuous parameter msc https://ems.press/doi/10.4171/173 cover image https://content.ems.press/assets/public/images/books/cover-142.jpg nam a22 5a 4500 10.4171/171 DE-4084 2017-01-12 a fot 00| 0| cr nn mmmmamaa 170112e20170112gw fot 00| 0|eng d 9783037196717 10.4171/171 doi DE-4084 PBMW bicssc 14Mxx msc 16Gxx msc 17Bxx msc 18Exx msc 20Gxx msc 22Exx msc 58Cxx msc 81Txx msc Krause edt Representation Theory - Current Trends and Perspectives. EMS Press 2017 1 online resource (773 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 11 2523-5168 Restricted to subscribers. https://ems.press/books From April 2009 until March 2016, the German Science Foundation supported generously the Priority Program SPP 1388 in Representation Theory. The core principles of the projects realized in the framework of the priority program have been categorification and geometrization, this is also reflected by the contributions to this volume. Apart from the articles by former postdocs supported by the priority program, the volume contains a number of invited research and survey articles, many of them are extended versions of talks given at the last joint meeting of the priority program in Bad Honnef in March 2015. This volume is covering current research topics from the representation theory of finite groups, of algebraic groups, of Lie superalgebras, of finite dimensional algebras and of infinite dimensional Lie groups. Graduate students and researchers in mathematics interested in representation theory will find this volume inspiring. It contains many stimulating contributions to the development of this broad and extremely diverse subject. Algebraic geometry bicssc Special varieties msc Representation theory of associative rings and algebras msc Lie algebras and Lie superalgebras msc Categorical algebra msc Linear algebraic groups and related topics msc Lie groups msc Calculus on manifolds; nonlinear operators msc Quantum field theory; related classical field theories msc Littelmann edt Malle edt Neeb edt Schweigert edt https://ems.press/doi/10.4171/171 cover image https://content.ems.press/assets/public/images/books/cover-143.jpg nam a22 5a 4500 10.4171/172 DE-4084 2017-03-23 a fot 00| 0| cr nn mmmmamaa 170323e20170323gw fot 00| 0|eng d 9783037196724 10.4171/172 doi DE-4084 PBKJ bicssc 35K05 msc 35Q30 msc 35Q92 msc 42B35 msc 46E35 msc 76D05 msc 92C15 msc 92C17 msc Triebel aut PDE Models for Chemotaxis and Hydrodynamics in Supercritical Function Spaces. EMS Press 2017 1 online resource (140 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 27 2523-5184 Restricted to subscribers. https://ems.press/books This book deals with PDE models for chemotaxis (the movement of biological cells or organisms in response of chemical gradients) and hydrodynamics (viscous, homogeneous, and incompressible fluid filling the entire space). The underlying Keller-Segel equations (chemotaxis), Navier-Stokes equations (hydrodynamics), and their numerous modifications and combinations are treated in the context of inhomogeneous spaces of Besov-Sobolev type paying special attention to mapping properties of related nonlinearities. Further models are considered, including (deterministic) Fokker-Planck equations and chemotaxis Navier-Stokes equations. These notes are addressed to graduate students and mathematicians having a working knowledge of basic elements of the theory of function spaces, especially of Besov-Sobolev type and interested in mathematical biology and physics. Differential calculus & equations bicssc Heat equation msc Navier-Stokes equations msc PDEs in connection with biology, chemistry and other natural sciences msc Function spaces arising in harmonic analysis msc Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems msc Navier-Stokes equations for incompressible viscous fluids msc Developmental biology, pattern formation msc Cell movement (chemotaxis, etc.) msc https://ems.press/doi/10.4171/172 cover image https://content.ems.press/assets/public/images/books/cover-144.jpg nam a22 5a 4500 10.4171/175 DE-4084 2017-05-05 a fot 00| 0| cr nn mmmmamaa 170505e20170505gw fot 00| 0|eng d 9783037196755 10.4171/175 doi DE-4084 PBKJ bicssc 81Q37 msc 81Q35 msc 35P15 msc 35P25 msc Dittrich edt Functional Analysis and Operator Theory for Quantum Physics ; The Pavel Exner Anniversary Volume. EMS Press 2017 1 online resource (595 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 12 2523-5168 Restricted to subscribers. https://ems.press/books This volume is dedicated to Pavel Exner on the occasion of his 70th anniversary. It collects contributions by numerous scientists with expertise in mathematical physics and in particular in problems arising from quantum mechanics. The questions addressed in the contributions cover a large range of topics. A lot of attention was paid to differential operators with zero range interactions, which are often used as models in quantum mechanics. Several authors considered problems related to systems with mixed-dimensions such as quantum waveguides, quantum layers and quantum graphs. Eigenvalues and eigenfunctions of Laplace and Schrödinger operators are discussed too, as well as systems with adiabatic time evolution. Although most of the problems treated in the book have a quantum mechanical background, some contributions deal with issues which go well beyond this framework; for example the Cayley-Hamilton theorem, approximation formulae for contraction semigroups or factorization of analytic operator-valued Fredholm functions. As for the mathematical tools involved, the book provides a wide variety of techniques from functional analysis and operator theory. Altogether the volume presents a collection of research papers which will be of interest to any active scientist working in one of the above mentioned fields. Differential calculus & equations bicssc Quantum dots, waveguides, ratchets, etc. msc Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices msc Estimates of eigenvalues in context of PDEs msc Scattering theory for PDEs msc Kovařík edt Laptev edt https://ems.press/doi/10.4171/175 cover image https://content.ems.press/assets/public/images/books/cover-145.jpg nam a22 5a 4500 10.4171/174 DE-4084 2017-05-12 a fot 00| 0| cr nn mmmmamaa 170512e20170512gw fot 00| 0|eng d 9783037196748 10.4171/174 doi DE-4084 PB bicssc PBF bicssc 16-01 msc 13E10 msc 15A63 msc 15A69 msc 16Dxx msc 16E10 msc 16E30 msc 16E40 msc 16G10 msc 16G20 msc 16G60 msc 16G70 msc 16S50 msc 16S70 msc 18A25 msc 18G15 msc Skowroński aut Frobenius Algebras II ; Tilted and Hochschild Extension Algebras. EMS Press 2017 1 online resource (629 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 18 2943-4955 Restricted to subscribers. https://ems.press/books This is the second of three volumes which will provide a comprehensive introduction to the modern representation theory of Frobenius algebras. The first part of the book is devoted to fundamental results of the representation theory of finite dimensional hereditary algebras and their tilted algebras, which allow to describe the representation theory of prominent classes of Frobenius algebras. The second part is devoted to basic classical and recent results concerning the Hochschild extensions of finite dimensional algebras by duality bimodules and their module categories. Moreover, the shapes of connected components of the stable Auslander-Reiten quivers of Frobenius algebras are described. The only prerequisite in this volume is a basic knowledge of linear algebra and some results of the first volume. It includes complete proofs of all results presented and provides a rich supply of examples and exercises. The text is primarily addressed to graduate students starting research in the representation theory of algebras as well mathematicians working in other fields. Mathematics bicssc Algebra bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras msc Commutative Artinian rings and modules, finite-dimensional algebras msc Quadratic and bilinear forms, inner products msc Multilinear algebra, tensor calculus msc Modules, bimodules and ideals in associative algebras msc Homological dimension in associative algebras msc Homological functors on modules (Tor, Ext, etc.) in associative algebras msc (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) msc Representations of associative Artinian rings msc Representations of quivers and partially ordered sets msc Representation type (finite, tame, wild, etc.) of associative algebras msc Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers msc Endomorphism rings; matrix rings msc Extensions of associative rings by ideals msc Functor categories, comma categories msc Ext and Tor, generalizations, Künneth formula (category-theoretic aspects) msc Yamagata aut https://ems.press/doi/10.4171/174 cover image https://content.ems.press/assets/public/images/books/cover-146.jpg nam a22 5a 4500 10.4171/176 DE-4084 2018-08-06 a fot 10| 0| cr nn mmmmamaa 180806e20180806gw fot 10| 0|eng d 9783037196762 10.4171/176 doi DE-4084 PB bicssc 00Bxx msc Mehrmann edt European Congress of Mathematics ; Berlin, July 18-22, 2016. EMS Press 2018 1 online resource (901 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books The European Congress of Mathematics, held every four years, is a well-established major international mathematical event. Following those in Paris (1992), Budapest (1996), Barcelona (2000), Stockholm (2004), Amsterdam (2008), and Kraków (2012), the Seventh European Congress of Mathematics (7ECM) took place in Berlin, Germany, July 18-22, 2016, with about 1100 participants from all over the world. Ten plenary, thirty-three invited and four special lectures formed the core of the program. As at all the previous EMS congresses, ten outstanding young mathematicians received the EMS prizes in recognition of their research achievements. In addition, two more prizes were awarded: The Felix Klein prize for a remarkable solution of an industrial problem, and - for the second time - the Otto Neugebauer Prize for a highly original and influential piece of work in the history of mathematics. The program was complemented by forty-three minisymposia with about 160 talks as well as contributed talks, spread over all areas of mathematics. Several panel discussions and meetings were organized, covering a variety of issues ranging from the future of mathematical publishing to public awareness of mathematics. These proceedings present extended versions of most of the plenary and invited lectures which were delivered during the congress, providing a permanent record of the best what mathematics offers today. Mathematics bicssc Conference proceedings and collections of articles msc Skutella edt https://ems.press/doi/10.4171/176 cover image https://content.ems.press/assets/public/images/books/cover-148.jpg nam a22 5a 4500 10.4171/177 DE-4084 2017-09-01 a fot 00| 0| cr nn mmmmamaa 170901e20170901gw fot 00| 0|eng d 9783037196779 10.4171/177 doi DE-4084 PBX bicssc 01A70 msc 01A60 msc 01A61 msc 01A80 msc 00A35 msc Raussen edt Interviews with the Abel Prize Laureates 2003-2016. EMS Press 2017 1 online resource (302 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books The Abel Prize was established in 2002 by the Norwegian Ministry of Education and Research. It has been awarded annually to mathematicians in recognition of pioneering scientific achievements. Since the first occasion in 2003, Martin Raussen and Christian Skau have had the opportunity to conduct extensive interviews with the laureates. The interviews were broadcast by Norwegian television; moreover, they have appeared in the membership journals of several mathematical societies. The interviews from the period 2003-2016 have now been collected in this edition. They highlight the mathematical achievements of the laureates in a historical perspective and they try to unravel the way in which the worlds most famous mathematicians conceive and judge their results, how they collaborate with peers and students, and how they perceive the importance of mathematics for society. History of mathematics bicssc Biographies, obituaries, personalia, bibliographies msc History of mathematics in the 20th century msc History of mathematics in the 21st century msc Sociology (and profession) of mathematics msc Methodology of mathematics msc Skau edt https://ems.press/doi/10.4171/177 cover image https://content.ems.press/assets/public/images/books/cover-147.jpg nam a22 5a 4500 10.4171/178 DE-4084 2018-02-15 a fot 00| 0| cr nn mmmmamaa 180215e20180215gw fot 00| 0|eng d 9783037196786 10.4171/178 doi DE-4084 PBK bicssc PBKJ bicssc PBMP bicssc 49Q10 msc 49Q05 msc 49Q12 msc 49K20 msc 49K40 msc 53A10 msc 35R35 msc 35J20 msc 58E25 msc 31B15 msc 65K10 msc 93B27 msc 74P20 msc 74P15 msc 74G65 msc 76M30 msc Henrot aut Shape Variation and Optimization ; A Geometrical Analysis. EMS Press 2018 1 online resource (379 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 28 2943-5005 Restricted to subscribers. https://ems.press/books Optimizing the shape of an object to make it the most efficient, resistant, streamlined, lightest, noiseless, stealthy or the cheapest is clearly a very old task. But the recent explosion of modeling and scientific computing have given this topic new life. Many new and interesting questions have been asked. A mathematical topic was born - shape optimization (or optimum design). This book provides a self-contained introduction to modern mathematical approaches to shape optimization, relying only on undergraduate level prerequisite but allowing to tackle open questions in this vibrant field. The analytical and geometrical tools and methods for the study of shapes are developed. In particular, the text presents a systematic treatment of shape variations and optimization associated with the Laplace operator and the classical capacity. Emphasis is also put on differentiation with respect to domains and a FAQ on the usual topologies of domains is provided. The book ends with geometrical properties of optimal shapes, including the case where they do not exist. Calculus & mathematical analysis bicssc Differential calculus & equations bicssc Differential & Riemannian geometry bicssc Optimization of shapes other than minimal surfaces msc Minimal surfaces and optimization msc Sensitivity analysis for optimization problems on manifolds msc Optimality conditions for problems involving partial differential equations msc Sensitivity, stability, well-posedness msc Minimal surfaces in differential geometry, surfaces with prescribed mean curvature msc Free boundary problems for PDEs msc Variational methods for second-order elliptic equations msc Applications of variational problems to control theory msc Potentials and capacities, extremal length and related notions in higher dimensions msc Numerical optimization and variational techniques msc Geometric methods msc Geometrical methods for optimization problems in solid mechanics msc Topological methods for optimization problems in solid mechanics msc Energy minimization in equilibrium problems in solid mechanics msc Variational methods applied to problems in fluid mechanics msc Pierre aut https://ems.press/doi/10.4171/178 cover image https://content.ems.press/assets/public/images/books/cover-149.png nam a22 5a 4500 10.4171/179 DE-4084 2017-07-11 a fot 00| 0| cr nn mmmmamaa 170711e20170711gw fot 00| 0|eng d 9783037196793 10.4171/179 doi DE-4084 PB bicssc 94-01 msc 12-01 msc Høholdt aut A Course In Error-Correcting Codes ; Second edition. EMS Press 2017 1 online resource (226 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 19 2943-4955 Restricted to subscribers. https://ems.press/books This book, updated and enlarged for the second edition, is written as a text for a course aimed at 3rd or 4th year students. Only some familiarity with elementary linear algebra and probability is directly assumed, but some maturity is required. The students may specialize in discrete mathematics, computer science, or communication engineering. The book is also a suitable introduction to coding theory for researchers from related fields or for professionals who want to supplement their theoretical basis. The book gives the coding basics for working on projects in any of the above areas, but material specific to one of these fields has not been included. The chapters cover the codes and decoding methods that are currently of most interest in research, development, and application. They give a relatively brief presentation of the essential results, emphasizing the interrelations between different methods and proofs of all important results. A sequence of problems at the end of each chapter serves to review the results and give the student an appreciation of the concepts. In addition, some problems and suggestions for projects indicate direction for further work. The presentation encourages the use of programming tools for studying codes, implementing decoding methods, and simulating performance. Specific examples of programming exercises are provided on the book's home page. *For the first edition of this book, please click [here](https://doi.org/10.4171/001).* Mathematics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory msc Justesen aut https://ems.press/doi/10.4171/179 cover image https://content.ems.press/assets/public/images/books/cover-150.jpg nam a22 5a 4500 10.4171/180 DE-4084 2017-07-25 a fot 00| 0| cr nn mmmmamaa 170725e20170725gw fot 00| 0|eng d 9783037196809 10.4171/180 doi DE-4084 PBPD bicssc 57R65 msc 32S55 msc Michel aut Higher-Dimensional Knots According to Michel Kervaire. EMS Press 2017 1 online resource (144 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 28 2523-5184 Restricted to subscribers. https://ems.press/books Michel Kervaire wrote six papers which can be considered fundamental to the development of higher-dimensional knot theory. They are not only of historical interest but naturally introduce to some of the essential techniques in this fascinating theory. This book is written to provide graduate students with the basic concepts necessary to read texts in higher-dimensional knot theory and its relations with singularities. The first chapters are devoted to a presentation of Pontrjagins construction, surgery and the work of Kervaire and Milnor on homotopy spheres. We pursue with Kervaires fundamental work on the group of a knot, knot modules and knot cobordism. We add developments due to Levine. Tools (like open books, handlebodies, plumbings, ) often used but hard to find in original articles are presented in appendices. We conclude with a description of the Kervaire invariant and the consequences of the Hill-Hopkins-Ravenel results in knot theory. Algebraic topology bicssc Surgery and handlebodies msc Milnor fibration; relations with knot theory msc Weber aut https://ems.press/doi/10.4171/180 cover image https://content.ems.press/assets/public/images/books/cover-151.jpg nam a22 5a 4500 10.4171/181 DE-4084 2018-05-25 a fot 00| 0| cr nn mmmmamaa 180525e20180525gw fot 00| 0|eng d 9783037196816 10.4171/181 doi DE-4084 PBP bicssc 22E66 msc 22E65 msc 60B15 msc 28C20 msc Kosyak aut Regular, Quasi-regular and Induced Representations of Infinite-dimensional Groups. EMS Press 2018 1 online resource (587 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 29 2943-5005 Restricted to subscribers. https://ems.press/books Almost all harmonic analysis on locally compact groups is based on the existence (and uniqueness) of a Haar measure. Therefore, it is very natural to attempt a similar construction for non-locally compact groups. The essential idea is to replace the non-existing Haar measure on an infinite-dimensional group by a suitable quasi-invariant measure on an appropriate completion of the initial group or on the completion of a homogeneous space. The aim of the book is a systematic development, by example, of noncommutative harmonic analysis on infinite-dimensional (non-locally compact) matrix groups. We generalize the notion of regular, quasi-regular and induced representations for arbitrary infinite-dimensional groups. The central idea to verify the irreducibility is the Ismagilov conjecture. We also extend the Kirillov orbit method for the group of upper triangular matrices of infinite order. In order to make the content accessible to a wide audience of nonspecialists, the exposition is essentially self-contained and very few prerequisites are needed. The book is aimed at graduate and advanced undergraduate students, as well as mathematicians who wish an introduction to representations of infinite-dimensional groups. Topology bicssc Analysis on and representations of infinite-dimensional Lie groups msc Infinite-dimensional Lie groups and their Lie algebras: general properties msc Probability measures on groups or semigroups, Fourier transforms, factorization msc Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) msc https://ems.press/doi/10.4171/181 cover image https://content.ems.press/assets/public/images/books/cover-152.jpg nam a22 5a 4500 10.4171/182 DE-4084 2018-01-21 a fot 00| 0| cr nn mmmmamaa 180121e20180121gw fot 00| 0|eng d 9783037196823 10.4171/182 doi DE-4084 PBMS bicssc 14-06 msc 32L10 msc 14M15 msc 55N91 msc 14C17 msc 14G17 msc Buczyński edt Schubert Varieties, Equivariant Cohomology and Characteristic Classes ; Impanga 15. EMS Press 2018 1 online resource (354 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 13 2523-5168 Restricted to subscribers. https://ems.press/books IMPANGA stands for the activities of Algebraic Geometers at the Institute of Mathematics, Polish Academy of Sciences, including one of the most important seminars in algebraic geometry in Poland. The topics of the lectures usually fit within the framework of complex algebraic geometry and neighboring areas of mathematics. This volume is a collection of contributions by the participants of the conference IMPANGA15, organized by participants of the seminar, as well as notes from the major lecture series of the seminar in the period 2010-2015. Both original research papers and self-contained expository surveys can be found here. The articles circulate around a broad range of topics within algebraic geometry such as vector bundles, Schubert varieties, degeneracy loci, homogeneous spaces, equivariant cohomology, Thom polynomials, characteristic classes, symmetric functions and polynomials, and algebraic geometry in positive characteristic. Analytic geometry bicssc Proceedings, conferences, collections, etc. pertaining to algebraic geometry msc Sheaves and cohomology of sections of holomorphic vector bundles, general results msc Grassmannians, Schubert varieties, flag manifolds msc Equivariant homology and cohomology in algebraic topology msc Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry msc Positive characteristic ground fields in algebraic geometry msc Michałek edt Postinghel edt https://ems.press/doi/10.4171/182 cover image https://content.ems.press/assets/public/images/books/cover-153.jpg nam a22 5a 4500 10.4171/135 DE-4084 2018-01-22 a fot 00| 0| cr nn mmmmamaa 180122e20180122gw fot 00| 0|eng d 9783037196359 10.4171/135 doi DE-4084 PB bicssc 11G99 msc 06E99 msc 13F30 msc 13J07 msc 14A15 msc 14A20 msc Fujiwara aut Foundations of Rigid Geometry I. EMS Press 2018 1 online resource (863 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Monographs in Mathematics (emm) 7 2523-5206 Restricted to subscribers. https://ems.press/books Rigid geometry is one of the modern branches of algebraic and arithmetic geometry. It has its historical origin in J. Tates rigid analytic geometry, which aimed at developing an analytic geometry over non-archimedean valued fields. Nowadays, rigid geometry is a discipline in its own right and has acquired vast and rich structures, based on discoveries of its relationship with birational and formal geometries. In this research monograph, foundational aspects of rigid geometry are discussed, putting emphasis on birational and topological features of rigid spaces. Besides the rigid geometry itself, topics include the general theory of formal schemes and formal algebraic spaces, based on a theory of complete rings which are not necessarily Noetherian. Also included is a discussion on the relationship with Tates original rigid analytic geometry, V.G. Berkovichs analytic geometry and R. Hubers adic spaces. As a model example of applications, a proof of Nagatas compactification theorem for schemes is given in the appendix. The book is encyclopedic and almost self-contained. Mathematics bicssc Arithmetic algebraic geometry (Diophantine geometry) msc Boolean algebras (Boolean rings) msc Valuation rings msc Analytical algebras and rings msc Schemes and morphisms msc Generalizations (algebraic spaces, stacks) msc Kato aut https://ems.press/doi/10.4171/135 cover image https://content.ems.press/assets/public/images/books/cover-154.jpg nam a22 5a 4500 10.4171/183 DE-4084 2018-03-14 a fot 00| 0| cr nn mmmmamaa 180314e20180314gw fot 00| 0|eng d 9783037196830 10.4171/183 doi DE-4084 PB bicssc 11-02 msc 11J86 msc 11Dxx msc 11B37 msc 11D25 msc 11D41 msc 11D59 msc 11D61 msc 11D75 msc 11D88 msc 11J25 msc 11J81 msc 11J82 msc Bugeaud aut Linear Forms in Logarithms and Applications. EMS Press 2018 1 online resource (240 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 28 2523-5141 Restricted to subscribers. https://ems.press/books The aim of this book is to serve as an introductory text to the theory of linear forms in the logarithms of algebraic numbers, with a special emphasis on a large variety of its applications. We wish to help students and researchers to learn what is hidden inside the blackbox Baker's theory of linear forms in logarithms (in complex or in p\-adic logarithms) and how this theory applies to many Diophantine problems, including the effective resolution of Diophantine equations, the abc\-conjecture, and upper bounds for the irrationality measure of some real numbers. Written for a broad audience, this accessible and self-contained book can be used for graduate courses (some 30 exercises are supplied). Specialists will appreciate the inclusion of over 30 open problems and the rich bibliography of over 450 references. Mathematics bicssc Research exposition (monographs, survey articles) pertaining to number theory msc Linear forms in logarithms; Baker's method msc Diophantine equations msc Recurrences msc Cubic and quartic Diophantine equations msc Higher degree equations; Fermat's equation msc Thue-Mahler equations msc Exponential Diophantine equations msc Diophantine inequalities msc \(p\)-adic and power series fields msc Diophantine inequalities msc Transcendence (general theory) msc Measures of irrationality and of transcendence msc https://ems.press/doi/10.4171/183 cover image https://content.ems.press/assets/public/images/books/cover-157.jpg nam a22 5a 4500 10.4171/184 DE-4084 2018-04-24 a fot 00| 0| cr nn mmmmamaa 180424e20180424gw fot 00| 0|eng d 9783037196847 10.4171/184 doi DE-4084 PBCD bicssc PBMW bicssc 03C45 msc 03C60 msc 03C98 msc 12J20 msc 12L12 msc 14E18 msc 20E18 msc Jahnke edt Lectures in Model Theory. EMS Press 2018 1 online resource (222 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Münster Lectures in Mathematics (mlm) 2 2523-5249 Restricted to subscribers. https://ems.press/books Model theory is a thriving branch of mathematical logic with strong connections to other fields of mathematics. Its versatility has recently led to spectacular applications in areas ranging from diophantine geometry, algebraic number theory and group theory to combinatorics. This volume presents lecture notes from a spring school in model theory which took place in Münster, Germany. The notes are aimed at PhD students but should also be accessible to undergraduates with some basic knowledge in model theory. They contain the core of stability theory (Bays, Palacín), two chapters connecting generalized stability theory with group theory (Clausen and Tent, Simon), as well as introductions to the model theory of valued fields (Hils, Jahnke) and motivic integration (Halupczok). Mathematical logic bicssc Algebraic geometry bicssc Classification theory, stability, and related concepts in model theory msc Model-theoretic algebra msc Applications of model theory msc General valuation theory for fields msc Model theory of fields msc Arcs and motivic integration msc Limits, profinite groups msc Palacín edt Tent edt https://ems.press/doi/10.4171/184 cover image https://content.ems.press/assets/public/images/books/cover-155.jpg nam a22 5a 4500 10.4171/185 DE-4084 2018-04-30 a fot 00| 0| cr nn mmmmamaa 180430e20180430gw fot 00| 0|eng d 9783037196854 10.4171/185 doi DE-4084 PB bicssc Kessar edt Local Representation Theory and Simple Groups. EMS Press 2018 1 online resource (369 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 29 2523-5184 Restricted to subscribers. https://ems.press/books The book contains extended versions of seven short lecture courses given during a semester programme on "Local Representation Theory and Simple Groups" held at the Centre Interfacultaire Bernoulli of the EPF Lausanne. These focussed on modular representation theory of finite groups, modern Clifford theoretic methods, the representation theory of finite reductive groups, as well as on various applications of character theory and representation theory, for example to base sizes and to random walks. These lectures are intended to form a good starting point for graduate students and researchers who wish to familiarize themselves with the foundations of the topics covered here. Furthermore they give an introduction to current research directions, including the state of some open problems in the field. Mathematics bicssc Malle edt Testerman edt https://ems.press/doi/10.4171/185 cover image https://content.ems.press/assets/public/images/books/cover-158.jpg nam a22 5a 4500 10.4171/186 DE-4084 2018-05-30 a fot 00| 0| cr nn mmmmamaa 180530e20180530gw fot 00| 0|eng d 9783037196861 10.4171/186 doi DE-4084 PBKJ bicssc 15B52 msc 35J10 msc 35L65 msc 35Q41 msc 35Q51 msc 35Q53 msc 37K10 msc 42B20 msc 46N20 msc 46N30 msc 46T12 msc 47B36 msc 47F05 msc 60H20 msc 68N30 msc 76S05 msc 33C45 msc 35A01 msc 35A02 msc 35L80 msc 37D45 msc 39A12 msc 47A10 msc 47N20 msc 47N30 msc 60B20 msc Gesztesy edt Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis ; The Helge Holden Anniversary Volume. EMS Press 2018 1 online resource (502 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 14 2523-5168 Restricted to subscribers. https://ems.press/books This volume is dedicated to Helge Holden on the occasion of his 60th anniversary. It collects contributions by numerous scientists with expertise in non-linear partial differential equations (PDEs), mathematical physics, and stochastic analysis, reflecting to a large degree Helge Holdens longstanding research interests. Accordingly, the problems addressed in the contributions deal with a large range of topics, including, in particular, infinite-dimensional analysis, linear and nonlinear PDEs, stochastic analysis, spectral theory, completely integrable systems, random matrix theory, and chaotic dynamics and sestina poetry. They represent to some extent the lectures presented at the conference _Non-linear PDEs, Mathematical Physics and Stochastic Analysis_, held at NTNU, Trondheim, July 4-7, 2016 (https://wiki.math.ntnu.no/holden60). The mathematical tools involved draw from a wide variety of techniques in functional analysis, operator theory, and probability theory. This collection of research papers will be of interest to any active scientist working in one of the above mentioned areas. Differential calculus & equations bicssc Random matrices (algebraic aspects) msc Schrödinger operator, Schrödinger equation msc Hyperbolic conservation laws msc Time-dependent Schrödinger equations and Dirac equations msc Soliton equations msc KdV equations (Korteweg-de Vries equations) msc Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) msc Singular and oscillatory integrals (Calderón-Zygmund, etc.) msc Applications of functional analysis to differential and integral equations msc Applications of functional analysis in probability theory and statistics msc Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds msc Jacobi (tridiagonal) operators (matrices) and generalizations msc General theory of partial differential operators msc Stochastic integral equations msc Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.) msc Flows in porous media; filtration; seepage msc Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) msc Existence problems for PDEs: global existence, local existence, non-existence msc Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness msc Degenerate hyperbolic equations msc Strange attractors, chaotic dynamics of systems with hyperbolic behavior msc Discrete version of topics in analysis msc Spectrum, resolvent msc Applications of operator theory to differential and integral equations msc Applications of operator theory in probability theory and statistics msc Random matrices (probabilistic aspects) msc Hanche-Olsen edt Jakobsen edt Lyubarskii edt Risebro edt Seip edt https://ems.press/doi/10.4171/186 cover image https://content.ems.press/assets/public/images/books/cover-162.jpg nam a22 5a 4500 10.4171/187 DE-4084 2018-06-15 a fot 00| 0| cr nn mmmmamaa 180615e20180615gw fot 00| 0|eng d 9783037196878 10.4171/187 doi DE-4084 PB bicssc 20G44 msc 20E42 msc 17B67 msc Marquis aut An Introduction to Kac-Moody Groups over Fields. EMS Press 2018 1 online resource (343 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 21 2943-4955 Restricted to subscribers. https://ems.press/books The interest for Kac-Moody algebras and groups has grown exponentially in the past decades, both in the mathematical and physics communities, and with it also the need for an introductory textbook on the topic. The aims of this book are twofold: \- to offer an accessible, reader-friendly and self-contained introduction to Kac-Moody algebras and groups; \- to clean the foundations and to provide a unified treatment of the theory. The book starts with an outline of the classical Lie theory, used to set the scene. Part II provides a self-contained introduction to Kac-Moody algebras. The heart of the book is Part III, which develops an intuitive approach to the construction and fundamental properties of Kac-Moody groups. It is complemented by two appendices, respectively offering introductions to affine group schemes and to the theory of buildings. Many exercises are included, accompanying the readers throughout their journey. The book assumes only a minimal background in linear algebra and basic topology, and is addressed to anyone interested in learning about Kac-Moody algebras and/or groups, from graduate (master) students to specialists. Mathematics bicssc Kac-Moody groups msc Groups with a \(BN\)-pair; buildings msc Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras msc https://ems.press/doi/10.4171/187 cover image https://content.ems.press/assets/public/images/books/cover-159.jpg nam a22 5a 4500 10.4171/188 DE-4084 2018-05-30 a fot 00| 0| cr nn mmmmamaa 180530e20180530gw fot 00| 0|eng d 9783037196885 10.4171/188 doi DE-4084 PBV bicssc 05-01 msc 05C50 msc 05C25 msc 11T24 msc 15A42 msc Nica aut A Brief Introduction to Spectral Graph Theory. EMS Press 2018 1 online resource (168 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 20 2943-4955 Restricted to subscribers. https://ems.press/books Spectral graph theory starts by associating matrices to graphs - notably, the adjacency matrix and the Laplacian matrix. The general theme is then, firstly, to compute or estimate the eigenvalues of such matrices, and secondly, to relate the eigenvalues to structural properties of graphs. As it turns out, the spectral perspective is a powerful tool. Some of its loveliest applications concern facts that are, in principle, purely graph theoretic or combinatorial. This text is an introduction to spectral graph theory, but it could also be seen as an invitation to algebraic graph theory. The first half is devoted to graphs, finite fields, and how they come together. This part provides an appealing motivation and context of the second, spectral, half. The text is enriched by many exercises and their solutions. The target audience are students from the upper undergraduate level onwards. We assume only a familiarity with linear algebra and basic group theory. Graph theory, finite fields, and character theory for abelian groups receive a concise overview and render the text essentially self-contained. Combinatorics & graph theory bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics msc Graphs and linear algebra (matrices, eigenvalues, etc.) msc Graphs and abstract algebra (groups, rings, fields, etc.) msc Other character sums and Gauss sums msc Inequalities involving eigenvalues and eigenvectors msc https://ems.press/doi/10.4171/188 cover image https://content.ems.press/assets/public/images/books/cover-156.jpg nam a22 5a 4500 10.4171/189 DE-4084 2018-05-25 a fot 00| 0| cr nn mmmmamaa 180525e20180525gw fot 00| 0|eng d 9783037196892 10.4171/189 doi DE-4084 PB bicssc 20F55 msc 20E42 msc 51E24 msc 57M07 msc Thomas aut Geometric and Topological Aspects of Coxeter Groups and Buildings. EMS Press 2018 1 online resource (160 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 24 2943-4971 Restricted to subscribers. https://ems.press/books Coxeter groups are groups generated by reflections, and they appear throughout mathematics. Tits developed the general theory of Coxeter groups in order to develop the theory of buildings. Buildings have interrelated algebraic, combinatorial and geometric structures, and are powerful tools for understanding the groups which act on them. These notes focus on the geometry and topology of Coxeter groups and buildings, especially nonspherical cases. The emphasis is on geometric intuition, and there are many examples and illustrations. Part I describes Coxeter groups and their geometric realisations, particularly the Davis complex, and Part II gives a concise introduction to buildings. This book will be suitable for mathematics graduate students and researchers in geometric group theory, as well as algebra and combinatorics. The assumed background is basic group theory, including group actions, and basic algebraic topology, together with some knowledge of Riemannian geometry. Mathematics bicssc Reflection and Coxeter groups (group-theoretic aspects) msc Groups with a \(BN\)-pair; buildings msc Buildings and the geometry of diagrams msc Topological methods in group theory msc https://ems.press/doi/10.4171/189 cover image https://content.ems.press/assets/public/images/books/cover-160.jpg nam a22 5a 4500 10.4171/198 DE-4084 2020-05-20 a fot 00| 0| cr nn mmmmamaa 200520e20200520gw fot 00| 0|eng d 9783037196984 10.4171/198 doi DE-4084 PB bicssc 11G09 msc 11J93 msc 11R58 msc 13A35 msc Böckle edt t-Motives: Hodge Structures, Transcendence and Other Motivic Aspects. EMS Press 2020 1 online resource (473 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 16 2523-5168 Restricted to subscribers. https://ems.press/books This volume contains research and survey articles on Drinfeld modules, Anderson t\-modules and t\-motives. Much material that had not been easily accessible in the literature is presented here, for example the cohomology theories and Pinks theory of Hodge structures attached to Drinfeld modules and t\-motives. Also included are survey articles on the function field analogue of Fontaines theory of p\-adic crystalline Galois representations and on transcendence methods over function fields, encompassing the theories of Frobenius difference equations, automata theory, and Mahlers method. In addition, this volume contains a small number of research articles on function field Iwasawa theory, 1-t\-motifs, and multizeta values. This book is a useful source for learning important techniques and an effective reference for all researchers working in or interested in the area of function field arithmetic, from graduate students to established experts. Mathematics bicssc Drinfel'd modules; higher-dimensional motives, etc. msc Transcendence theory of Drinfel'd and \(t\)-modules msc Arithmetic theory of algebraic function fields msc Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure msc Goss edt Hartl edt Papanikolas edt https://ems.press/doi/10.4171/198 cover image https://content.ems.press/assets/public/images/books/cover-164.jpg nam a22 5a 4500 10.4171/190 DE-4084 2018-09-30 a fot 00| 0| cr nn mmmmamaa 180930e20180930gw fot 00| 0|eng d 9783037196908 10.4171/190 doi DE-4084 PBKJ bicssc 35J40 msc 31B15 msc 31B25 msc Maz'ya aut Boundary Behavior of Solutions to Elliptic Equations in General Domains. EMS Press 2018 1 online resource (441 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 30 2943-5005 Restricted to subscribers. https://ems.press/books The present book is a detailed exposition of the author and his collaborators work on boundedness, continuity, and differentiability properties of solutions to elliptic equations in general domains, that is, in domains that are not a priori restricted by assumptions such as piecewise smoothness or being a Lipschitz graph. The description of the boundary behavior of such solutions is one of the most difficult problems in the theory of partial differential equations. After the famous Wiener test, the main contributions to this area were made by the author. In particular, necessary and sufficient conditions for the validity of imbedding theorems are given, which provide criteria for the unique solvability of boundary value problems of second and higher order elliptic equations. Another striking result is a test for the regularity of a boundary point for polyharmonic equations. The book will be interesting and useful for a wide audience. It is intended for specialists and graduate students working in the theory of partial differential equations. Differential calculus & equations bicssc Boundary value problems for higher-order elliptic equations msc Potentials and capacities, extremal length and related notions in higher dimensions msc Boundary behavior of harmonic functions in higher dimensions msc https://ems.press/doi/10.4171/190 cover image https://content.ems.press/assets/public/images/books/cover-161.jpg nam a22 5a 4500 10.4171/191 DE-4084 2019-01-31 a fot 00| 0| cr nn mmmmamaa 190131e20190131gw fot 00| 0|eng d 9783037196915 10.4171/191 doi DE-4084 PBKJ bicssc 35G05 msc 35S05 msc Gel'man aut Estimates for Differential Operators in Half-space ; Translated from the German by Darya Apushkinskaya. EMS Press 2019 1 online resource (264 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 31 2943-5005 Restricted to subscribers. https://ems.press/books Inequalities for differential operators play a fundamental role in the modern theory of partial differential equations. Among the numerous applications of such inequalities are existence and uniqueness theorems, error estimates for numerical approximations of solutions and for residual terms in asymptotic formulas, as well as results on the structure of the spectrum. The inequalities cover a wide range of differential operators, boundary conditions and norms of the corresponding function spaces. The book focuses on estimates up to the boundary of a domain. It contains a great variety of inequalities for differential and pseudodifferential operators with constant coefficients. Results of final character are obtained, without any restrictions on the type of differential operators. Algebraic necessary and sufficient conditions for the validity of the corresponding a priori estimates are presented. General criteria are systematically applied to particular types of operators found in classical equations and systems of mathematical physics (such as Lames system of static elasticity theory or the linearized Navier-Stokes system), Cauchy-Riemanns operators, Schrödinger operators, among others. The well-known results of Aronszajn, Agmon-Douglis-Nirenberg and Schechter fall into the general scheme, and sometimes are strengthened. The book will be interesting and useful to a wide audience, including graduate students and specialists in the theory of differential equations. Differential calculus & equations bicssc Linear higher-order PDEs msc Pseudodifferential operators as generalizations of partial differential operators msc Maz'ya aut https://ems.press/doi/10.4171/191 cover image https://content.ems.press/assets/public/images/books/cover-163.jpg nam a22 5a 4500 10.4171/192 DE-4084 2019-01-07 a fot 00| 0| cr nn mmmmamaa 190107e20190107gw fot 00| 0|eng d 9783037196922 10.4171/192 doi DE-4084 PBKJ bicssc 35L67 msc 35L04 msc 35L65 msc 76L05 msc 76N15 msc Christodoulou aut The Shock Development Problem. EMS Press 2019 1 online resource (932 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Monographs in Mathematics (emm) 8 2523-5206 Restricted to subscribers. https://ems.press/books This monograph addresses the problem of the development of shocks in the context of the Eulerian equations of the mechanics of compressible fluids. The mathematical problem is that of an initial-boundary value problem for a nonlinear hyperbolic system of partial differential equations with a free boundary and singular initial conditions. The free boundary is the shock hypersurface and the boundary conditions are jump conditions relative to a prior solution, conditions following from the integral form of the mass, momentum and energy conservation laws. The prior solution is provided by the authors previous work which studies the maximal classical development of smooth initial data. New geometric and analytic methods are introduced to solve the problem. Geometry enters as the acoustical structure, a Lorentzian metric structure defined on the spacetime manifold by the fluid. This acoustical structure interacts with the background spacetime structure. Reformulating the equations as two coupled first order systems, the characteristic system, which is fully nonlinear, and the wave system, which is quasilinear, a complete regularization of the problem is achieved. Geometric methods also arise from the need to treat the free boundary. These methods involve the concepts of bi-variational stress and of variation fields. The main new analytic method arises from the need to handle the singular integrals appearing in the energy identities. Shocks being an ubiquitous phenomenon, occuring also in magnetohydrodynamics, nonlinear elasticity, and the electrodynamics of noninear media, the methods developed in this monograph are likely to be found relevant in these fields as well. Differential calculus & equations bicssc Shocks and singularities for hyperbolic equations msc Initial-boundary value problems for first-order hyperbolic equations msc Hyperbolic conservation laws msc Shock waves and blast waves in fluid mechanics msc Gas dynamics (general theory) msc https://ems.press/doi/10.4171/192 cover image https://content.ems.press/assets/public/images/books/cover-165.jpg nam a22 5a 4500 10.4171/193 DE-4084 2019-04-08 a fot 00| 0| cr nn mmmmamaa 190408e20190408gw fot 00| 0|eng d 9783037196939 10.4171/193 doi DE-4084 PHDF bicssc PB bicssc 76P05 msc 76W05 msc 82C40 msc 35B25 msc Arsénio aut From the Vlasov-Maxwell-Boltzmann System to Incompressible Viscous Electro-magneto-hydrodynamics. Volume I EMS Press 2019 1 online resource (418 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Monographs in Mathematics (emm) 9 2523-5206 Restricted to subscribers. https://ems.press/books The Vlasov-Maxwell-Boltzmann system is a microscopic model to describe the dynamics of charged particles subject to self-induced electromagnetic forces. At the macroscopic scale, in the incompressible viscous fluid limit the evolution of the plasma is governed by equations of Navier-Stokes-Fourier type, with some electromagnetic forcing that may take on various forms depending on the number of species and on the strength of the interactions. From the mathematical point of view, these models have very different behaviors. Their analysis therefore requires various mathematical methods which this book aims to present in a systematic, painstaking, and exhaustive way. The first part of this work is devoted to the systematic formal analysis of viscous hydrodynamic limits of the Vlasov-Maxwell-Boltzmann system, leading to a precise classification of physically relevant models for viscous incompressible plasmas, some of which have not previously been described in the literature. In the second part, the convergence results are made precise and rigorous, assuming the existence of renormalized solutions for the Vlasov-Maxwell-Boltzmann system. The analysis is based essentially on the scaled entropy inequality. Important mathematical tools are introduced, with new developments used to prove these convergence results (Chapman-Enskog-type decomposition and regularity in the v variable, hypoelliptic transfer of compactness, analysis of high frequency time oscillations, and more). The third and fourth parts (which will be published in a second volume) show how to adapt the arguments presented in the conditional case to deal with a weaker notion of solutions to the Vlasov-Maxwell-Boltzmann system, the existence of which is known. Fluid mechanics bicssc Mathematics bicssc Rarefied gas flows, Boltzmann equation in fluid mechanics msc Magnetohydrodynamics and electrohydrodynamics msc Kinetic theory of gases in time-dependent statistical mechanics msc Singular perturbations in context of PDEs msc Saint-Raymond aut https://ems.press/doi/10.4171/193 cover image https://content.ems.press/assets/public/images/books/cover-166.jpg nam a22 5a 4500 10.4171/195 DE-4084 2019-01-31 a fot 00| 0| cr nn mmmmamaa 190131e20190131gw fot 00| 0|eng d 9783037196953 10.4171/195 doi DE-4084 PB bicssc 46-02 msc 46E35 msc 42C40 msc 42B35 msc 41A55 msc Triebel aut Function Spaces with Dominating Mixed Smoothness. EMS Press 2019 1 online resource (210 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 30 2523-5184 Restricted to subscribers. https://ems.press/books The first part of this book is devoted to function spaces in Euclidean n\-space with dominating mixed smoothness. Some new properties are derived and applied in the second part where weighted spaces with dominating mixed smoothness in arbitrary bounded domains in Euclidean n\-space are introduced and studied. This includes wavelet frames, numerical integration and discrepancy, measuring the deviation of sets of points from uniformity. These notes are addressed to graduate students and mathematicians having a working knowledge of basic elements of the theory of function spaces, especially of Besov-Sobolev type. In particular, it will be of interest for researchers dealing with approximation theory, numerical integration and discrepancy. Mathematics bicssc Research exposition (monographs, survey articles) pertaining to functional analysis msc Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems msc Nontrigonometric harmonic analysis involving wavelets and other special systems msc Function spaces arising in harmonic analysis msc Approximate quadratures msc https://ems.press/doi/10.4171/195 cover image https://content.ems.press/assets/public/images/books/cover-167.jpg nam a22 5a 4500 10.4171/196 DE-4084 2019-02-27 a fot 00| 0| cr nn mmmmamaa 190227e20190227gw fot 00| 0|eng d 9783037196960 10.4171/196 doi DE-4084 PB bicssc PBCD bicssc 03B30 msc 51A05 msc 51F15 msc 51F20 msc 51M04 msc 51M05 msc 51M09 msc 51M10 msc 51M16 msc 51M20 msc 51M25 msc 51N15 msc 52A15 msc 52A55 msc 52B15 msc 52C25 msc 05C62 msc 53-01 msc 53A05 msc 53A35 msc 53C35 msc 53C45 msc Alberge edt Eighteen Essays in Non-Euclidean Geometry. EMS Press 2019 1 online resource (475 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 29 2523-5141 Restricted to subscribers. https://ems.press/books This book consists of a series of self-contained essays in non-Euclidean geometry in a broad sense, including the classical geometries of constant curvature (spherical and hyperbolic), de Sitter, anti-de Sitter, co-Euclidean, co-Minkowski, Hermitian geometries, and some axiomatically defined geometries. Some of these essays deal with very classical questions and others address problems that are at the heart of present day research, but all of them are concerned with fundamental topics. All the essays are self-contained and most of them can be understood by the general educated mathematician. They should be useful to researchers and to students of non-Euclidean geometry, and they are intended to be references for the various topics they present. Mathematics bicssc Mathematical logic bicssc Foundations of classical theories (including reverse mathematics) msc General theory of linear incidence geometry and projective geometries msc Reflection groups, reflection geometries msc Congruence and orthogonality in metric geometry msc Elementary problems in Euclidean geometries msc Euclidean geometries (general) and generalizations msc Elementary problems in hyperbolic and elliptic geometries msc Hyperbolic and elliptic geometries (general) and generalizations msc Inequalities and extremum problems in real or complex geometry msc Polyhedra and polytopes; regular figures, division of spaces msc Length, area and volume in real or complex geometry msc Projective analytic geometry msc Convex sets in \(3\) dimensions (including convex surfaces) msc Spherical and hyperbolic convexity msc Symmetry properties of polytopes msc Rigidity and flexibility of structures (aspects of discrete geometry) msc Graph representations (geometric and intersection representations, etc.) msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry msc Surfaces in Euclidean and related spaces msc Non-Euclidean differential geometry msc Differential geometry of symmetric spaces msc Global surface theory (convex surfaces à la A. D. Aleksandrov) msc Papadopoulos edt https://ems.press/doi/10.4171/196 cover image https://content.ems.press/assets/public/images/books/cover-168.jpg nam a22 5a 4500 10.4171/197 DE-4084 2019-07-05 a fot 00| 0| cr nn mmmmamaa 190705e20190705gw fot 00| 0|eng d 9783037196977 10.4171/197 doi DE-4084 P bicssc PBK bicssc PB bicssc 58J65 msc 52C23 msc 20F65 msc 11M41 msc 46L54 msc 60J45 msc 35C07 msc 35Q55 msc 43A25 msc 20F36 msc 11R42 msc 14L05 msc Baake edt Spectral Structures and Topological Methods in Mathematics. EMS Press 2019 1 online resource (433 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 15 2523-5168 Restricted to subscribers. https://ems.press/books This book is a collection of survey articles about spectral structures and the application of topological methods bridging different mathematical disciplines, from pure to applied. The topics are based on work done in the Collaborative Research Centre (SFB) 701. Notable examples are non-crossing partitions, which connect representation theory, braid groups, non-commutative probability as well as spectral distributions of random matrices. The local distributions of such spectra are universal, also representing the local distribution of zeros of L\-functions in number theory. An overarching method is the use of zeta functions in the asymptotic counting of sublattices, group representations etc. Further examples connecting probability, analysis, dynamical systems and geometry are generating operators of deterministic or stochastic processes, stochastic differential equations, and fractals, relating them to the local geometry of such spaces and the convergence to stable and semi-stable states. Mathematics & science bicssc Calculus & mathematical analysis bicssc Mathematics bicssc Diffusion processes and stochastic analysis on manifolds msc Quasicrystals and aperiodic tilings in discrete geometry msc Geometric group theory msc Other Dirichlet series and zeta functions msc Free probability and free operator algebras msc Probabilistic potential theory msc Traveling wave solutions msc NLS equations (nonlinear Schrödinger equations) msc Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups msc Braid groups; Artin groups msc Zeta functions and \(L\)-functions of number fields msc Formal groups, \(p\)-divisible groups msc Götze edt Hoffmann edt https://ems.press/doi/10.4171/197 cover image https://content.ems.press/assets/public/images/books/cover-169.jpg nam a22 5a 4500 10.4171/094 DE-4084 2019-11-15 a fot 00| 0| cr nn mmmmamaa 191115e20191115gw fot 00| 0|eng d 9783037195949 10.4171/094 doi DE-4084 PB bicssc 81T13 msc 35L10 msc 35L40 msc 58J40 msc 81T28 msc 35L15 msc 35L45 msc 58J47 msc 53C50 msc Gérard aut Microlocal Analysis of Quantum Fields on Curved Spacetimes. EMS Press 2019 1 online resource (228 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda ESI Lectures in Mathematics and Physics (esi) 10 2943-4939 Restricted to subscribers. https://ems.press/books We focus on free fields and the corresponding quasi-free states and more precisely on Klein-Gordon fields and Dirac fields. The first chapters are devoted to preliminary material on CCR\*-algebras, quasi-free states, wave equations on Lorentzian manifolds, microlocal analysis and to the important _Hadamard condition_, characterizing physically acceptable quantum states on curved spacetimes. In the later chapters more advanced tools of microlocal analysis, like the global pseudo-differential calculus on non-compact manifolds, are used to construct and study Hadamard states for Klein-Gordon fields by various methods, in particular by scattering theory and by Wick rotation arguments. In the last chapter the fermionic theory of free Dirac quantum fields on Lorentzian manifolds is described in some detail. This monograph is addressed to both mathematicians and mathematical physicists. The first will be able to use it as a rigorous exposition of free quantum fields on curved spacetimes and as an introduction to some interesting and physically important problems arising in this domain. The second may find this text a useful introduction and motivation to the use of more advanced tools of microlocal analysis in this area of research. Mathematics bicssc Yang-Mills and other gauge theories in quantum field theory msc Second-order hyperbolic equations msc First-order hyperbolic systems msc Pseudodifferential and Fourier integral operators on manifolds msc Thermal quantum field theory msc Initial value problems for second-order hyperbolic equations msc Initial value problems for first-order hyperbolic systems msc Propagation of singularities; initial value problems on manifolds msc Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics msc https://ems.press/doi/10.4171/094 cover image https://content.ems.press/assets/public/images/books/cover-173.jpg nam a22 5a 4500 10.4171/199 DE-4084 2019-11-08 a fot 00| 0| cr nn mmmmamaa 191108e20191108gw fot 00| 0|eng d 9783037196991 10.4171/199 doi DE-4084 P bicssc PB bicssc 01-XX msc Jaëck edt Gösta Mittag-Leffler and Vito Volterra. 40 Years of Correspondence. EMS Press 2019 1 online resource (438 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 12 2523-5222 Restricted to subscribers. https://ems.press/books The present book contains the voluminous correspondence exchanged between the Swedish mathematician Gösta Mittag-Leffler and his younger Italian colleague Vito Volterra spanning a period of almost forty years at the end of the 19th and beginning of the 20th centuries. The relationship between the two men is remarkable for both personal and scientific reasons. Mittag-Leffler met Volterra for the first time as a brilliant young student of Ulisse Dini in Pisa. He was soon captivated by the creativity and the skills of the young man, and eventually became his mentor. Being himself at the center of a major scientific network, Mittag-Leffler introduced Volterra to the major mathematicians of the time, especially the Germans (Weierstrass, Klein, Cantor) and French (Darboux, Jordan). In a few years, Volterra became the most prominent Italian mathematician and forged his own network of scientists all over Europe, and even in the United States which he was one of the first major European mathematicians to visit. Despite their difference in age, both men developed a deep and faithful friendship and their letters reflect the variety of themes of their exchanges. Of course, mathematics was the most prominent, and both men often used the letters as a first draft of their ideas and the addressee as a first judge of their soundness. Besides mathematics, they also touched upon many aspects of both private and public life: matrimony, children, holidays, politics and so on. This vast set of letters affords the reader a general overview of mathematical life at the turn of the 19th century and an appreciation of the European intellectual spirit which came to an end, or at least suffered a drastic turn, when the Great War broke out. Volterra and Mittag-Lefflers exchanges illustrate how general analysis, especially functional analysis, gained a dramatic momentum during those years, and how Volterra became one of the major leaders of the topic, opening the path for several fundamental developments over the following decades. Through the letters one can follow the institutional career and scientific activity of both Volterra and Mittag-Leffler who shared many details about their situation. The four editors are all specialists in the history of mathematics of the considered period. An extensive general introduction to the correspondence explains the context and the conditions in which it was developed. Moreover, the original letters are annotated with a large number of footnotes, which provide a broader cultural picture from these captivating documents. Mathematics & science bicssc Mathematics bicssc History and biography msc Mazliak edt Sallent Del Colombo edt Tazzioli edt https://ems.press/doi/10.4171/199 cover image https://content.ems.press/assets/public/images/books/cover-171.jpg nam a22 5a 4500 10.4171/200 DE-4084 2019-12-10 a fot 00| 0| cr nn mmmmamaa 191210e20191210gw fot 00| 0|eng d 9783037197004 10.4171/200 doi DE-4084 PBKJ bicssc 37D40 msc 37D20 msc 37A30 msc 37A35 msc Fisher aut Hyperbolic Flows. EMS Press 2019 1 online resource (737 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 25 2943-4971 Restricted to subscribers. https://ems.press/books The origins of dynamical systems trace back to flows and differential equations, and this is a modern text and reference on dynamical systems in which continuous-time dynamics is primary. It addresses needs unmet by modern books on dynamical systems, which largely focus on discrete time. Students have lacked a useful introduction to flows, and researchers have difficulty finding references to cite for core results in the theory of flows. Even when these are known substantial diligence and consultation with experts is often needed to find them. This book presents the theory of flows from the topological, smooth, and measurable points of view. The first part introduces the general topological and ergodic theory of flows, and the second part presents the core theory of hyperbolic flows as well as a range of recent developments. Therefore, the book can be used both as a textbook - for either courses or self-study - and as a reference for students and researchers. There are a number of new results in the book, and many more are hard to locate elsewhere, often having appeared only in the original research literature. This book makes them all easily accessible and does so in the context of a comprehensive and coherent presentation of the theory of hyperbolic flows. Differential calculus & equations bicssc Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) msc Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) msc Ergodic theorems, spectral theory, Markov operators msc Entropy and other invariants, isomorphism, classification in ergodic theory msc Hasselblatt aut https://ems.press/doi/10.4171/200 cover image https://content.ems.press/assets/public/images/books/cover-170.jpg nam a22 5a 4500 10.4171/automata DE-4084 2021-09-13 a fot 00| 0| cr nn mmmmamaa 210913e20210913gw fot 00| 0|eng d 9783985475063 10.4171/automata doi DE-4084 P bicssc PB bicssc 68Q45 msc Pin edt Handbook of Automata Theory. EMS Press 2021 1 online resource (1608 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books Automata theory is a subject of study at the crossroads of mathematics, theoretical computer science, and applications. In its core it deals with abstract models of systems whose behaviour is based on transitions between states, and it develops methods for the description, classification, analysis, and design of such systems. The _Handbook of Automata Theory_ gives a comprehensive overview of current research in automata theory, and is aimed at a broad readership of researchers and graduate students in mathematics and computer science. Volume I is divided into three parts. The first part presents various types of automata: automata on words, on infinite words, on finite and infinite trees, weighted and maxplus automata, transducers, and two-dimensional models. Complexity aspects are discussed in the second part. Algebraic and topological aspects of automata theory are covered in the third part. Volume II consists of two parts. The first part is dedicated to applications of automata in mathematics: group theory, number theory, symbolic dynamics, logic, and real functions. The second part presents a series of further applications of automata theory such as message-passing systems, symbolic methods, synthesis, timed automata, verification of higher-order programs, analysis of probabilistic processes, natural language processing, formal verification of programs and quantum computing. The two volumes comprise a total of thirty-nine chapters, with extensive references and individual tables of contents for each one, as well as a detailed subject index. Mathematics & science bicssc Mathematics bicssc Formal languages and automata msc https://ems.press/doi/10.4171/automata cover image https://content.ems.press/assets/public/images/books/cover-172.jpg nam a22 5a 4500 10.4171/automata-1 DE-4084 2021-09-13 a fot 00| 0| cr nn mmmmamaa 210913e20210913gw fot 00| 0|eng d 9783985475025 10.4171/automata-1 doi DE-4084 P bicssc PB bicssc 68Q45 msc Pin edt Handbook of Automata Theory. Volume I. Theoretical Foundations EMS Press 2021 1 online resource (1608 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books Automata theory is a subject of study at the crossroads of mathematics, theoretical computer science, and applications. In its core it deals with abstract models of systems whose behaviour is based on transitions between states, and it develops methods for the description, classification, analysis, and design of such systems. The _Handbook of Automata Theory_ gives a comprehensive overview of current research in automata theory, and is aimed at a broad readership of researchers and graduate students in mathematics and computer science. Volume I is divided into three parts. The first part presents various types of automata: automata on words, on infinite words, on finite and infinite trees, weighted and maxplus automata, transducers, and two-dimensional models. Complexity aspects are discussed in the second part. Algebraic and topological aspects of automata theory are covered in the third part. Volume II consists of two parts. The first part is dedicated to applications of automata in mathematics: group theory, number theory, symbolic dynamics, logic, and real functions. The second part presents a series of further applications of automata theory such as message-passing systems, symbolic methods, synthesis, timed automata, verification of higher-order programs, analysis of probabilistic processes, natural language processing, formal verification of programs and quantum computing. The two volumes comprise a total of thirty-nine chapters, with extensive references and individual tables of contents for each one, as well as a detailed subject index. Mathematics & science bicssc Mathematics bicssc Formal languages and automata msc https://ems.press/doi/10.4171/automata-1 cover image https://content.ems.press/assets/public/images/books/cover-174.png nam a22 5a 4500 10.4171/automata-2 DE-4084 2021-09-13 a fot 00| 0| cr nn mmmmamaa 210913e20210913gw fot 00| 0|eng d 9783985475032 10.4171/automata-2 doi DE-4084 P bicssc PB bicssc 68Q45 msc Pin edt Handbook of Automata Theory. Volume II. Automata in Mathematics and Selected Applications EMS Press 2021 1 online resource (1608 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books Automata theory is a subject of study at the crossroads of mathematics, theoretical computer science, and applications. In its core it deals with abstract models of systems whose behaviour is based on transitions between states, and it develops methods for the description, classification, analysis, and design of such systems. The _Handbook of Automata Theory_ gives a comprehensive overview of current research in automata theory, and is aimed at a broad readership of researchers and graduate students in mathematics and computer science. Volume I is divided into three parts. The first part presents various types of automata: automata on words, on infinite words, on finite and infinite trees, weighted and maxplus automata, transducers, and two-dimensional models. Complexity aspects are discussed in the second part. Algebraic and topological aspects of automata theory are covered in the third part. Volume II consists of two parts. The first part is dedicated to applications of automata in mathematics: group theory, number theory, symbolic dynamics, logic, and real functions. The second part presents a series of further applications of automata theory such as message-passing systems, symbolic methods, synthesis, timed automata, verification of higher-order programs, analysis of probabilistic processes, natural language processing, formal verification of programs and quantum computing. The two volumes comprise a total of thirty-nine chapters, with extensive references and individual tables of contents for each one, as well as a detailed subject index. Mathematics & science bicssc Mathematics bicssc Formal languages and automata msc https://ems.press/doi/10.4171/automata-2 cover image https://content.ems.press/assets/public/images/books/cover-175.png nam a22 5a 4500 10.4171/203 DE-4084 2020-02-15 a fot 00| 0| cr nn mmmmamaa 200215e20200215gw fot 00| 0|eng d 9783037197035 10.4171/203 doi DE-4084 PB bicssc 30F60 msc 32G15 msc 30C20 msc 14H60 msc 30C35 msc 30C62 msc 30C70 msc 30C75 msc 57M50 msc 01A60 msc 01A55 msc 20F65 msc 20F67 msc 22E40 msc 30D30 msc 30D35 msc 30F45 msc Papadopoulos edt Handbook of Teichmüller Theory, Volume VII. EMS Press 2020 1 online resource (626 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 30 2523-5141 Restricted to subscribers. https://ems.press/books The present volume of the Handbook of Teichmüller theory is divided into three parts. The first part contains surveys on various topics in Teichmüller theory, including the complex structure of Teichmüller space, the Deligne-Mumford compactification of the moduli space, holomorphic quadratic differentials, Kleinian groups, hyperbolic 3-manifolds and the ending lamination theorem, the universal Teichmüller space, barycentric extensions of maps of the circle, and the theory of Higgs bundles. The second part consists of three historico-geometrical articles on Tissot (a precursor of the theory of quasiconfomal mappings), Grötzsch and Lavrentieff, the two main founders of the modern theory of quasiconformal mappings. The third part comprises English translations of five papers by Grötzsch, a paper by Lavrentieff, and three papers by Teichmüller. These nine papers are foundational essays on the theories of conformal invariants and quasiconformal mappings, with applications to conformal geometry, to the type problem and to Nevanlinna's theory. The papers are followed by commentaries that highlight the relations between them and between later works on the subject. These papers are not only historical documents; they constitute an invaluable source of ideas for current research in Teichmüller theory. Mathematics bicssc Teichmüller theory for Riemann surfaces msc Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) msc Conformal mappings of special domains msc Vector bundles on curves and their moduli msc General theory of conformal mappings msc Quasiconformal mappings in the complex plane msc Extremal problems for conformal and quasiconformal mappings, variational methods msc Extremal problems for conformal and quasiconformal mappings, other methods msc General geometric structures on low-dimensional manifolds msc History of mathematics in the 20th century msc History of mathematics in the 19th century msc Geometric group theory msc Hyperbolic groups and nonpositively curved groups msc Discrete subgroups of Lie groups msc Meromorphic functions of one complex variable (general theory) msc Value distribution of meromorphic functions of one complex variable, Nevanlinna theory msc Conformal metrics (hyperbolic, Poincaré, distance functions) msc https://ems.press/doi/10.4171/203 cover image https://content.ems.press/assets/public/images/books/cover-176.jpg nam a22 5a 4500 10.4171/204 DE-4084 2020-02-28 a fot 00| 0| cr nn mmmmamaa 200228e20200228gw fot 00| 0|eng d 9783037197042 10.4171/204 doi DE-4084 PB bicssc PBKJ bicssc 05Exx msc 81T15 msc 81T18 msc 81Q30 msc 34C20 msc 37C10 msc 34M40 msc 34M60 msc 11M32 msc 30D60 msc Chapoton edt Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA). Volume I EMS Press 2020 1 online resource (354 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 31 2523-5141 Restricted to subscribers. https://ems.press/books This is volume 1 of a 2-volume work comprising a total of 14 refereed research articles which stem from the CARMA Conference (Algebraic Combinatorics, Resurgence, Moulds and Applications), held at the Centre International de Rencontres Mathématiques in Luminy, France, from June 26 to 30, 2017. The conference did notably emphasise the role of Hopf algebraic techniques and related concepts (e.g. Rota-Baxter algebras, operads, Ecalles mould calculus) which have lately proved pervasive in combinatorics, but also in many other fields, from multiple zeta values to the algebraic study of control systems and the theory of rough paths. The volumes should be useful to researchers or graduate students in mathematics working in these domains and to theoretical physicists involved with resurgent functions and alien calculus. Mathematics bicssc Differential calculus & equations bicssc Algebraic combinatorics msc Perturbative methods of renormalization applied to problems in quantum field theory msc Feynman diagrams msc Feynman integrals and graphs; applications of algebraic topology and algebraic geometry msc Transformation and reduction of ordinary differential equations and systems, normal forms msc Dynamics induced by flows and semiflows msc Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain msc Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) msc Multiple Dirichlet series and zeta functions and multizeta values msc Quasi-analytic and other classes of functions of one complex variable msc Fauvet edt Malvenuto edt Thibon edt https://ems.press/doi/10.4171/204 cover image https://content.ems.press/assets/public/images/books/cover-180.jpg nam a22 5a 4500 10.4171/205 DE-4084 2020-02-28 a fot 00| 0| cr nn mmmmamaa 200228e20200228gw fot 00| 0|eng d 9783037197059 10.4171/205 doi DE-4084 PB bicssc 05Exx msc 81T15 msc 81T18 msc 81Q30 msc 34C20 msc 37C10 msc 34M40 msc 34M60 msc 11M32 msc 30D60 msc Chapoton edt Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA). Volume II EMS Press 2020 1 online resource (396 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 32 2523-5141 Restricted to subscribers. https://ems.press/books This is volume 2 of a 2-volume work comprising a total of 14 refereed research articles which stem from the CARMA Conference (Algebraic Combinatorics, Resurgence, Moulds and Applications), held at the Centre International de Rencontres Mathématiques in Luminy, France, from June 26 to 30, 2017. The conference did notably emphasise the role of Hopf algebraic techniques and related concepts (e.g. Rota-Baxter algebras, operads, Ecalles mould calculus) which have lately proved pervasive in combinatorics, but also in many other fields, from multiple zeta values to the algebraic study of control systems and the theory of rough paths. The volumes should be useful to researchers or graduate students in mathematics working in these domains and to theoretical physicists involved with resurgent functions and alien calculus. Mathematics bicssc Algebraic combinatorics msc Perturbative methods of renormalization applied to problems in quantum field theory msc Feynman diagrams msc Feynman integrals and graphs; applications of algebraic topology and algebraic geometry msc Transformation and reduction of ordinary differential equations and systems, normal forms msc Dynamics induced by flows and semiflows msc Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain msc Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) msc Multiple Dirichlet series and zeta functions and multizeta values msc Quasi-analytic and other classes of functions of one complex variable msc Fauvet edt Malvenuto edt Thibon edt https://ems.press/doi/10.4171/205 cover image https://content.ems.press/assets/public/images/books/cover-178.jpg nam a22 5a 4500 10.4171/206 DE-4084 2020-08-06 a fot 00| 0| cr nn mmmmamaa 200806e20200806gw fot 00| 0|eng d 9783037197066 10.4171/206 doi DE-4084 PBKJ bicssc 35-02 msc 35J20 msc 35J50 msc 35J60 msc 35J88 msc 49M29 msc 65N15 msc 65N85 msc 74K20 msc Repin aut Accuracy of Mathematical Models ; Dimension Reduction, Homogenization, and Simplification. EMS Press 2020 1 online resource (333 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 33 2943-5005 Restricted to subscribers. https://ems.press/books The expansion of scientific knowledge and the development of technology are strongly connected with quantitative analysis of mathematical models. Accuracy and reliability are the key properties we wish to understand and control. This book presents a unified approach to the analysis of accuracy of deterministic mathematical models described by variational problems and partial differential equations of elliptic type. It is based on new mathematical methods developed to estimate the distance between a solution of a boundary value problem and any function in the admissible functional class associated with the problem in question. The theory is presented for a wide class of elliptic variational problems. It is applied to the investigation of modelling errors arising in dimension reduction, homogenization, simplification, and various conversion methods (penalization, linearization, regularization, etc.). A collection of examples illustrates the performance of error estimates. Differential calculus & equations bicssc Research exposition (monographs, survey articles) pertaining to partial differential equations msc Variational methods for second-order elliptic equations msc Variational methods for elliptic systems msc Nonlinear elliptic equations msc Unilateral problems for elliptic systems and systems of variational inequalities with elliptic operators msc Numerical methods involving duality msc Error bounds for boundary value problems involving PDEs msc Fictitious domain methods for boundary value problems involving PDEs msc Plates msc Sauter aut https://ems.press/doi/10.4171/206 cover image https://content.ems.press/assets/public/images/books/cover-177.jpg nam a22 5a 4500 10.4171/207 DE-4084 2020-06-05 a fot 00| 0| cr nn mmmmamaa 200605e20200605gw fot 00| 0|eng d 9783037197073 10.4171/207 doi DE-4084 PBW bicssc U bicssc PB bicssc 68U07 msc 76B75 msc 93C05 msc 90C11 msc 90C30 msc 65L80 msc 90-08 msc 90-10 msc 90-11 msc Morsi edt Decision Support Systems for Water Supply Systems ; Smart Water System to Improve the Operation of Water Supply Systems by Using Applied Mathematics. EMS Press 2020 1 online resource (243 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series in Industrial and Applied Mathematics (esiam) 2 2523-5095 Restricted to subscribers. https://ems.press/books Operating water supply systems is complex. Engineers must ensure that consumers are reliably supplied with a sufficient quantity and quality of water, as well as a sufficient water pressure at all times - all while maintaining reasonable prices. This book summarizes the results of the German BMBF (Federal Ministry of Education and Research) funded joint research project, EWave (Project ID: 02WER1323F), that was initiated to develop an innovative Decision Support System (DSS) for water supply companies. For decision making and operational support, the EWave system uses newly developed integrated optimization modules. As a result, the user receives operating schedules on a 15 minute scale. To achieve this, mixed-integer linear and nonlinear mathematical optimization methods are combined. First, a mixed-integer optimization model is solved in order to derive all discrete decisions (primarily pump schedules). The aim is to approximate the physics by piecewise linear relaxations sufficiently to optimize decisions. EWave then uses nonlinear optimization and simulation methods to verify the physics. The process is iterated as necessary. This approach enables globally optimal solutions within an a priori given quality tolerance. Optimization results obtained in real time yield a potential of energy savings of up to 4-6% daily for the waterworks in the pilot area. This book was written for automation experts in water supply companies as well as mathematicians who work for infrastructure companies. Applied mathematics bicssc Computing & information technology bicssc Mathematics bicssc Computer science aspects of computer-aided design msc Flow control and optimization for incompressible inviscid fluids msc Linear systems in control theory msc Mixed integer programming msc Nonlinear programming msc Numerical methods for differential-algebraic equations msc Computational methods for problems pertaining to operations research and mathematical programming msc Mathematical modeling or simulation for problems pertaining to operations research and mathematical programming msc Research data for problems pertaining to operations research and mathematical programming msc Pirsing edt https://ems.press/doi/10.4171/207 cover image https://content.ems.press/assets/public/images/books/cover-179.jpg nam a22 5a 4500 10.4171/208 DE-4084 2020-03-31 a fot 00| 0| cr nn mmmmamaa 200331e20200331gw fot 00| 0|eng d 9783037197080 10.4171/208 doi DE-4084 PBMS bicssc 14J28 msc 14C34 msc 14J10 msc 14J15 msc 14J50 msc 32G20 msc Kondō aut K3 Surfaces. EMS Press 2020 1 online resource (250 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 32 2943-5005 Restricted to subscribers. https://ems.press/books K3 surfaces are a key piece in the classification of complex analytic or algebraic surfaces. The term was coined by A. Weil in 1958 - a result of the initials Kummer, Kähler, Kodaira, and the mountain K2 found in Karakoram. The most famous example is the Kummer surface discovered in the 19th century. K3 surfaces can be considered as a 2-dimensional analogue of an elliptic curve, and the theory of periods - called the Torelli-type theorem for K3 surfaces - was established around 1970. Since then, several pieces of research on K3 surfaces have been undertaken and more recently K3 surfaces have even become of interest in theoretical physics. The main purpose of this book is an introduction to the Torelli-type theorem for complex analytic K3 surfaces, and its applications. The theory of lattices and their reflection groups is necessary to study K3 surfaces, and this book introduces these notions. The book contains, as well as lattices and reflection groups, the classification of complex analytic surfaces, the Torelli-type theorem, the subjectivity of the period map, Enriques surfaces, an application to the moduli space of plane quartics, finite automorphisms of K3 surfaces, Niemeier lattices and the Mathieu group, the automorphism group of Kummer surfaces and the Leech lattice. The author seeks to demonstrate the interplay between several sorts of mathematics and hopes the book will prove helpful to researchers in algebraic geometry and related areas, and to graduate students with a basic grounding in algebraic geometry. Analytic geometry bicssc \(K3\) surfaces and Enriques surfaces msc Torelli problem msc Families, moduli, classification: algebraic theory msc Moduli, classification: analytic theory; relations with modular forms msc Automorphisms of surfaces and higher-dimensional varieties msc Period matrices, variation of Hodge structure; degenerations msc https://ems.press/doi/10.4171/208 cover image https://content.ems.press/assets/public/images/books/cover-181.jpg nam a22 5a 4500 10.4171/209 DE-4084 2020-08-04 a fot 00| 0| cr nn mmmmamaa 200804e20200804gw fot 00| 0|eng d 9783037197097 10.4171/209 doi DE-4084 P bicssc PB bicssc 20J05 msc 18B40 msc 55P91 msc 18M30 msc 18N10 msc 18N25 msc 18N40 msc 19A22 msc 20C99 msc Balmer aut Mackey 2-Functors and Mackey 2-Motives. EMS Press 2020 1 online resource (235 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Monographs in Mathematics (emm) 10 2523-5206 Restricted to subscribers. https://ems.press/books This book is dedicated to equivariant mathematics, specifically the study of additive categories of objects with actions of finite groups. The framework of Mackey 2-functors axiomatizes the variance of such categories as a function of the group. In other words, it provides a categorification of the widely used notion of Mackey functor, familiar to representation theorists and topologists. The book contains an extended catalogue of examples of such Mackey 2-functors that are already in use in many mathematical fields from algebra to topology, from geometry to KK-theory. Among the first results of the theory, the ambidexterity theorem gives a way to construct further examples and the separable monadicity theorem explains how the value of a Mackey 2-functor at a subgroup can be carved out of the value at a larger group, by a construction that generalizes ordinary localization in the same way that the étale topology generalizes the Zariski topology. The second part of the book provides a motivic approach to Mackey 2-functors, 2-categorifying the well-known span construction of Dress and Lindner. This motivic theory culminates with the following application: The idempotents of Yoshidas crossed Burnside ring are the universal source of block decompositions. The book is self-contained, with appendices providing extensive background and terminology. It is written for graduate students and more advanced researchers interested in category theory, representation theory and topology. Mathematics & science bicssc Mathematics bicssc Homological methods in group theory msc Groupoids, semigroupoids, semigroups, groups (viewed as categories) msc Equivariant homotopy theory in algebraic topology msc String diagrams and graphical calculi msc 2-categories, bicategories, double categories msc Categorification msc Homotopical algebra, Quillen model categories, derivators msc Frobenius induction, Burnside and representation rings msc Representation theory of groups msc Dell'Ambrogio aut https://ems.press/doi/10.4171/209 cover image https://content.ems.press/assets/public/images/books/cover-182.jpg nam a22 5a 4500 10.4171/210 DE-4084 2020-06-30 a fot 00| 0| cr nn mmmmamaa 200630e20200630gw fot 00| 0|eng d 9783037197103 10.4171/210 doi DE-4084 PBMW bicssc 14J26 msc 14J27 msc 14J28 msc 14J29 msc 14E05 msc 14E07 msc 14E30 msc 14N05 msc 14J10 msc Ciliberto aut Classification of Complex Algebraic Surfaces. EMS Press 2020 1 online resource (143 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 31 2523-5184 Restricted to subscribers. https://ems.press/books he classification of complex algebraic surfaces is a very classical subject which goes back to the old Italian school of algebraic geometry with Enriques and Castelnuovo. However, the exposition in the present book is modern and follows Mori's approach to the classification of algebraic varieties. The text includes the P_{12} theorem, the Sarkisov programme in the surface case and the Noether-Castelnuovo theorem in its classical version. This book serves as a relatively quick and handy introduction to the theory of algebraic surfaces and is intended for readers with a good knowledge of basic algebraic geometry. Although an acquaintance with the basic parts of books like _Principles of Algebraic Geometry_ by Griffiths and Harris or _Algebraic Geometry_ by Hartshorne should be sufficient, the author strove to make the text as self-contained as possible and, for this reason, a first chapter is devoted to a quick exposition of some preliminaries. Algebraic geometry bicssc Rational and ruled surfaces msc Elliptic surfaces, elliptic or Calabi-Yau fibrations msc \(K3\) surfaces and Enriques surfaces msc Surfaces of general type msc Rational and birational maps msc Birational automorphisms, Cremona group and generalizations msc Minimal model program (Mori theory, extremal rays) msc Projective techniques in algebraic geometry msc Families, moduli, classification: algebraic theory msc https://ems.press/doi/10.4171/210 cover image https://content.ems.press/assets/public/images/books/cover-183.jpg nam a22 5a 4500 10.4171/211 DE-4084 2020-10-09 a fot 00| 0| cr nn mmmmamaa 201009e20201009gw fot 00| 0|eng d 9783037197110 10.4171/211 doi DE-4084 PBK bicssc 37K55 msc 37K50 msc 35L05 msc 35Q55 msc Berti aut Quasi-Periodic Solutions of Nonlinear Wave Equations on the d-Dimensional Torus. EMS Press 2020 1 online resource (374 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Monographs in Mathematics (emm) 11 2523-5206 Restricted to subscribers. https://ems.press/books Many partial differential equations (PDEs) arising in physics, such as the nonlinear wave equation and the Schrödinger equation, can be viewed as infinite-dimensional Hamiltonian systems. In the last thirty years, several existence results of time quasi-periodic solutions have been proved adopting a "dynamical systems" point of view. Most of them deal with equations in one space dimension, whereas for multidimensional PDEs a satisfactory picture is still under construction. An updated introduction to the now rich subject of KAM theory for PDEs is provided in the first part of this research monograph. We then focus on the nonlinear wave equation, endowed with periodic boundary conditions. The main result of the monograph proves the bifurcation of small amplitude finite-dimensional invariant tori for this equation, in any space dimension. This is a difficult small divisor problem due to complex resonance phenomena between the normal mode frequencies of oscillations. The proof requires various mathematical methods, ranging from Nash-Moser and KAM theory to reduction techniques in Hamiltonian dynamics and multiscale analysis for quasi-periodic linear operators, which are presented in a systematic and self-contained way. Some of the techniques introduced in this monograph have deep connections with those used in Anderson localization theory. This book will be useful to researchers who are interested in small divisor problems, particularly in the setting of Hamiltonian PDEs, and who wish to get acquainted with recent developments in the field. Calculus & mathematical analysis bicssc Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems msc Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems msc Wave equation msc NLS equations (nonlinear Schrödinger equations) msc Bolle aut https://ems.press/doi/10.4171/211 cover image https://content.ems.press/assets/public/images/books/cover-184.jpg nam a22 5a 4500 10.4171/zlam/26 DE-4084 2021-03-31 a fot 00| 0| cr nn mmmmamaa 210331e20210331gw fot 00| 0|eng d 9783985475001 10.4171/zlam/26 doi DE-4084 P bicssc PB bicssc PB bicssc 57K20 msc Baader aut Geometry and Topology of Surfaces. EMS Press 2021 1 online resource (86 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 26 2943-4971 Restricted to subscribers. https://ems.press/books These lecture notes cover the classification of hyperbolic structures and measured foliations on surfaces in a minimalist way. While the inspiration is obviously taken from the excellent books _Primer on mapping class groups_ and _Travaux de Thurston sur les surfaces_, the author aimed at including a little bit more of hyperbolic trigonometry, including a proof of Basmajian's identity on the orthogeodesic spectrum, while keeping the rest short. Mathematics & science bicssc Mathematics bicssc Mathematics bicssc 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) msc https://ems.press/doi/10.4171/zlam/26 cover image https://content.ems.press/assets/public/images/books/cover-185.jpg nam a22 5a 4500 10.4171/elm/32 DE-4084 2021-04-01 a fot 00| 0| cr nn mmmmamaa 210401e20210401gw fot 00| 0|eng d 9783985475049 10.4171/elm/32 doi DE-4084 PB bicssc 46L10 msc 46L51 msc Hiai aut Lectures on Selected Topics in von Neumann Algebras. EMS Press 2021 1 online resource (250 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 32 2523-5184 Restricted to subscribers. https://ems.press/books The theory of von Neumann algebras, originating with the work of F. J. Murray and J. von Neumann in the late 1930s, has grown into a rich discipline with connections to different branches of mathematics and physics. Following the breakthrough of Tomita-Takesaki theory, many great advances were made throughout the 1970s by H. Araki, A. Connes, U. Haagerup, M. Takesaki and others. These lecture notes aim to present a fast-track study of some important topics in classical parts of von Neumann algebra theory that were developed in the 1970s. Starting with Tomita-Takesaki theory, this book covers topics such as the standard form, Connes cocycle derivatives, operator-valued weights, type III structure theory and non-commutative integration theory. The self-contained presentation of the material makes this book useful not only to graduate students and researchers who want to know the fundamentals of von Neumann algebras, but also to interested undergraduates who have a basic knowledge of functional analysis and measure theory. Mathematics bicssc General theory of von Neumann algebras msc Noncommutative measure and integration msc https://ems.press/doi/10.4171/elm/32 cover image https://content.ems.press/assets/public/images/books/cover-188.jpg nam a22 5a 4500 10.4171/ecr/17 DE-4084 2021-05-31 a fot 00| 0| cr nn mmmmamaa 210531e20210531gw fot 00| 0|eng d 9783985475056 10.4171/ecr/17 doi DE-4084 P bicssc PB bicssc 92D15 msc 60-XX msc Baake edt Probabilistic Structures in Evolution. EMS Press 2021 1 online resource (502 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 17 2523-5168 Restricted to subscribers. https://ems.press/books The present volume collects twenty-one survey articles about probabilistic aspects of biological evolution. They cover a large variety of topics from the research done within the German Priority Programme SPP 1590. Evolution is a complex phenomenon driven by various processes, such as mutation and recombination of genetic material, reproduction of individuals, and selection of favourable types. These processes all have intrinsically random elements, which give rise to a wealth of phenomena that cannot be explained by deterministic models. Examples of such effects are the loss of genetic variability due to random reproduction and the emergence of random genealogies. The collection is centred around the stochastic processes in population genetics and population dynamics. On the one hand, these are individual-based models of predator-prey and of coevolution type, of adaptive dynamics, or of experimental evolution, considered in the usual forward direction of time. They lead to processes describing the evolution of type frequencies, which may then be analysed via suitable limit theorems. On the other hand, one traces the ancestral lines of individuals back into the past; this leads to random genealogies. Beyond the classical concept of Kingman's coalescent, emphasis is on genealogies with multiple mergers and on ancestral structures that take into account selection, recombination, or migration. The contributions in this volume will be valuable to researchers interested in stochastic processes and their biological applications, or in mathematical population biology. Mathematics & science bicssc Mathematics bicssc Problems related to evolution msc Probability theory and stochastic processes msc Wakolbinger edt https://ems.press/doi/10.4171/ecr/17 cover image https://content.ems.press/assets/public/images/books/cover-186.jpg nam a22 5a 4500 10.4171/ecr/18 DE-4084 2021-06-15 a fot 00| 0| cr nn mmmmamaa 210615e20210615gw fot 00| 0|eng d 9783985475070 10.4171/ecr/18 doi DE-4084 P bicssc PB bicssc 34L15 msc 34L40 msc 35J10 msc 35P05 msc 35P15 msc 35P20 msc 44A10 msc 47A10 msc 47A63 msc 47B28 msc 47F10 msc 81Q10 msc Exner edt Partial Differential Equations, Spectral Theory, and Mathematical Physics ; The Ari Laptev Anniversary Volume. EMS Press 2021 1 online resource (494 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 18 2523-5168 Restricted to subscribers. https://ems.press/books This volume is dedicated to Ari Laptev on the occasion of his 70th birthday. It collects contributions by his numerous colleagues sharing with him research interests in analysis and spectral theory. In brief, the topics covered include Friedrichs, Hardy, and Lieb-Thirring inequalities, eigenvalue bounds and asymptotics, Feshbach-Schur maps and perturbation theory, scattering theory and orthogonal polynomials, stability of matter, electron density estimates, Bose-Einstein condensation, Wehrl-type entropy inequalities, Bogoliubov theory, wave packet evolution, heat kernel estimates, homogenization, d-bar problems, Brezis-Nirenberg problems, the nonlinear Schrödinger equation in magnetic fields, classical discriminants, and the two-dimensional Euler-Bardina equations. In addition, Aris multifaceted service to the mathematical community is also touched upon. Altogether the volume presents a collection of research articles which will be of interest to any active scientist working in one of the above mentioned fields. Mathematics & science bicssc Mathematics bicssc Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators msc Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) msc Schrödinger operator, Schrödinger equation msc General topics in linear spectral theory for PDEs msc Estimates of eigenvalues in context of PDEs msc Asymptotic distributions of eigenvalues in context of PDEs msc Laplace transform msc Spectrum, resolvent msc Linear operator inequalities msc Nonselfadjoint operators msc Elliptic operators and their generalizations msc Selfadjoint operator theory in quantum theory, including spectral analysis msc Frank edt Gesztesy edt Holden edt Weidl edt https://ems.press/doi/10.4171/ecr/18 cover image https://content.ems.press/assets/public/images/books/cover-187.jpg nam a22 5a 4500 10.4171/irma/33 DE-4084 2021-07-15 a fot 00| 0| cr nn mmmmamaa 210715e20210715gw fot 00| 0|eng d 9783985475018 10.4171/irma/33 doi DE-4084 P bicssc PB bicssc 01-02 msc 16T05 msc 17B37 msc 17B63 msc 18M05 msc 20D60 msc 53D17 msc 57K31 msc 55N33 msc 68R15 msc 57R19 msc 57R56 msc 58D19 msc Papadopoulos edt Topology and Geometry ; A Collection of Essays Dedicated to Vladimir G. Turaev. EMS Press 2021 1 online resource (698 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 33 2523-5141 Restricted to subscribers. https://ems.press/books The present volume consists of a collection of essays dedicated to Vladimir Turaev. The essays cover the large spectrum of topics in which Turaev has been interested, including knot and link invariants, quantum representations, TQFTs, state sum constructions, geometric structures on knot complements, Kleinian groups, geometric group theory and its relationship with 3-manifolds, mapping class groups, operads, mathematical physics, Grothendiecks program, the philosophy of mathematics, and several other topics. At the same time, this volume will give an overview of topics that are at the forefront of current research in topology and geometry. Some of the essays are research articles and contain new results, sometimes answering questions that were raised by Turaev. The rest of the essays are surveys that will introduce the reader to some key ideas in the field. Mathematics & science bicssc Mathematics bicssc Research exposition (monographs, survey articles) pertaining to history and biography msc Hopf algebras and their applications msc Quantum groups (quantized enveloping algebras) and related deformations msc Poisson algebras msc Monoidal categories, symmetric monoidal categories msc Arithmetic and combinatorial problems involving abstract finite groups msc Poisson manifolds; Poisson groupoids and algebroids msc Invariants of 3-manifolds (including skein modules, character varieties) msc Intersection homology and cohomology in algebraic topology msc Combinatorics on words msc Algebraic topology on manifolds and differential topology msc Topological quantum field theories (aspects of differential topology) msc Group actions and symmetry properties msc https://ems.press/doi/10.4171/irma/33 cover image https://content.ems.press/assets/public/images/books/cover-189.jpg nam a22 5a 4500 10.4171/etb/22 DE-4084 2021-08-02 a fot 00| 0| cr nn mmmmamaa 210802e20210802gw fot 00| 0|eng d 9783985475100 10.4171/etb/22 doi DE-4084 P bicssc 49Q22 msc 60B05 msc 28A33 msc 35A15 msc 35Q35 msc 49N15 msc 28A50 msc Figalli aut An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows. EMS Press 2021 1 online resource (144 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 22 2943-4955 Restricted to subscribers. https://ems.press/books This book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this beautiful subject. The presentation focuses on the essential topics of the theory: Kantorovich duality, existence and uniqueness of optimal transport maps, Wasserstein distances, the JKO scheme, Ottos calculus, and Wasserstein gradient flows. At the end, a presentation of some selected applications of optimal transport is given. The book is suitable for a course at the graduate level, and also includes an appendix with a series of exercises along with their solutions. This book has appeared in a [second edition](https://doi.org/10.4171/etb/25) in 2023. Mathematics & science bicssc Optimal transportation msc Probability measures on topological spaces msc Spaces of measures, convergence of measures msc Variational methods applied to PDEs msc PDEs in connection with fluid mechanics msc Duality theory (optimization) msc Integration and disintegration of measures msc Glaudo aut https://ems.press/doi/10.4171/etb/22 cover image https://content.ems.press/assets/public/images/books/cover-190.jpg nam a22 5a 4500 10.4171/elm/33 DE-4084 2021-08-02 a fot 00| 0| cr nn mmmmamaa 210802e20210802gw fot 00| 0|eng d 9783985475087 10.4171/elm/33 doi DE-4084 P bicssc PB bicssc 33-01 msc 33C45 msc 42C05 msc 15A23 msc 33C47 msc 34B24 msc 65D30 msc García-Ardila aut Orthogonal Polynomials and Linear Functionals ; An Algebraic Approach and Applications. EMS Press 2021 1 online resource (128 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 33 2523-5184 Restricted to subscribers. https://ems.press/books This book presents an introduction to orthogonal polynomials, with an algebraic flavor, based on linear functionals defining the orthogonality and the Jacobi matrices associated with them. Basic properties of their zeros as well as quadrature rules are discussed. A key point is the analysis of those functionals satisfying Pearson equations (semiclassical case) and the hierarchy based on their class. The book's structure reflects the fact that its content is based on a set of lectures delivered by one of the authors at the first Orthonet Summer School in Seville, Spain in 2016. The presentation of the material is self-contained and will be valuable to students and researchers interested in a novel approach to the study of orthogonal polynomials, focusing on their analytic properties. Mathematics & science bicssc Mathematics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions msc Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) msc Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis msc Factorization of matrices msc Other special orthogonal polynomials and functions msc Sturm-Liouville theory msc Numerical integration msc Marcellán aut Marriaga aut https://ems.press/doi/10.4171/elm/33 cover image https://content.ems.press/assets/public/images/books/cover-191.jpg nam a22 5a 4500 10.4171/etb/23 DE-4084 2021-10-11 a fot 00| 0| cr nn mmmmamaa 211011e20211011gw fot 00| 0|eng d 9783985475124 10.4171/etb/23 doi DE-4084 PBKQ bicssc PBU bicssc 49-01 msc 49L20 msc 49N90 msc 90C39 msc Cannarsa aut Dynamic Optimization for Beginners ; With Prerequisites and Applications. EMS Press 2021 1 online resource (360 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 23 2943-4955 Restricted to subscribers. https://ems.press/books Nowadays, optimization problems for dynamical systems enter more and more the basic knowledge required to approach applied sciences, engineering, and social sciences. On the other hand, even the results of most common use in this field, known as dynamic optimization, assume familiarity with an advanced mathematical background which may at times be perceived as discouraging. The main purpose of this book is to give interested readers a friendly introduction to this subject, providing them with the essential notions needed to handle most of the concrete situations they will be faced with. The main topics covered are calculus of variations, optimal control theory, and dynamic programming. As explained above, the book aims to be of interest both to mathematics students and to students or researchers in other disciplines such as economics and data science, who wish to use dynamic optimization in a conscientious way. The contents are self-contained and all the prerequisites may be found in the first chapters. Many applications are discussed and a large number of examples and exercises, both proposed and solved, complements the theory. Calculus of variations bicssc Optimization bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control msc Dynamic programming in optimal control and differential games msc Applications of optimal control and differential games msc Dynamic programming msc Gazzola aut https://ems.press/doi/10.4171/etb/23 cover image https://content.ems.press/assets/public/images/books/cover-192.jpg nam a22 5a 4500 10.4171/etm/34 DE-4084 2021-11-22 a fot 00| 0| cr nn mmmmamaa 211122e20211122gw fot 00| 0|eng d 9783985475094 10.4171/etm/34 doi DE-4084 P bicssc PB bicssc 35Q35 msc 76M50 msc 76T20 msc 35B27 msc Khruslov aut Homogenized Models of Suspension Dynamics. EMS Press 2021 1 online resource (288 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 34 2943-5005 Restricted to subscribers. https://ems.press/books This book studies the motion of suspensions, that is, of mixtures of a viscous incompressible fluid with small solid particles that can interact with each other through forces of non-hydrodynamic origin. In view of the complexity of the original (microscopic) system of equations that describe such phenomena, which appear both in nature and in engineering processes, the problem is reduced to a macroscopic description of the motion of mixtures as an effective continuous medium. The focus is on developing mathematical methods for constructing such homogenized models for the motion of suspensions with an arbitrary distribution of solid particles in a fluid. In particular, the results presented establish that depending on the concentration of the solid phase of the mixture, the motion of suspensions can occur in two qualitatively different modes: that of frozen or of filtering particles. Being one of the first mathematically rigorous treatises on suspensions from the viewpoint of homogenization theory, this book will be useful to graduate students and researchers in applied analysis and partial differential equations as well as to physicists and engineers interested in the theory of complex fluids with microstructure. Mathematics & science bicssc Mathematics bicssc PDEs in connection with fluid mechanics msc Homogenization applied to problems in fluid mechanics msc Suspensions msc Homogenization in context of PDEs; PDEs in media with periodic structure msc https://ems.press/doi/10.4171/etm/34 cover image https://content.ems.press/assets/public/images/books/cover-193.jpg nam a22 5a 4500 10.4171/elm/34 DE-4084 2022-04-19 a fot 00| 0| cr nn mmmmamaa 220419e20220419gw fot 00| 0|eng d 9783985475148 10.4171/elm/34 doi DE-4084 P bicssc PB bicssc Berglund aut An Introduction to Singular Stochastic PDEs ; Allen-Cahn Equations, Metastability, and Regularity Structures. EMS Press 2022 1 online resource (230 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 33 2523-5184 Restricted to subscribers. https://ems.press/books Stochastic partial differential equations (SPDEs) model the evolution in time of spatially extended systems subject to a random driving. Recent years have witnessed tremendous progress in the theory of so-called singular SPDEs. These equations feature a singular, distribution-valued driving term, a typical example being spacetime white noise, which makes them ill-posed as such. In many cases, it is however possible to make sense of these equations by applying a so-called renormalisation procedure, initially introduced in quantum field theory. This book gives a largely self-contained exposition of the subject of regular and singular SPDEs in the particular case of the Allen-Cahn equation, which models phase separation. Properties of the equation are discussed successively in one, two and three spatial dimensions, allowing to introduce new difficulties of the theory in an incremental way. In addition to existence and uniqueness of solutions, aspects of long-time dynamics such as invariant measures and metastability are discussed. A large part of the last chapter, about the three-dimensional case, is dedicated to the theory of regularity structures, which has been developed by Martin Hairer and co-authors in the last years, and allows to describe a large class of singular SPDEs. The book is intended for graduate students and researchers in mathematics and physics with prior knowledge in stochastic processes or stochastic calculus. Mathematics & science bicssc Mathematics bicssc https://ems.press/doi/10.4171/elm/34 cover image https://content.ems.press/assets/public/images/books/cover-232.png nam a22 5a 4500 10.4171/mems/1 DE-4084 2022-05-05 a fot 00| 0| cr nn mmmmamaa 220505e20220505gw fot 00| 0|eng d 9783985475209 10.4171/mems/1 doi DE-4084 PB bicssc 35L71 msc 35B35 msc 35B40 msc 35P25 msc 35S50 msc Delort aut Long-Time Dispersive Estimates for Perturbations of a Kink Solution of One-Dimensional Cubic Wave Equations. EMS Press 2022 1 online resource (292 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 1 2747-9099 Open Access https://ems.press/books A kink is a stationary solution to a cubic one-dimensional wave equation {(\partial_t^2-\partial_x^2)\phi \phi-\phi^3} that has different limits when {x} goes to {-\infty} and {+\infty}, like {H(x) \tanh(\frac{x}{\sqrt{2}})}. Asymptotic stability of this solution under small odd perturbation in the energy space has been studied in a recent work of Kowalczyk, Martel and Muñoz. They have been able to show that the perturbation may be written as the sum {a(t)Y(x) +\psi(t,x)}, where {Y} is a function in Schwartz space, {a(t)} a function of time having some decay properties at infinity, and {\psi(t,x)} satisfies some *local in space* dispersive estimate. These results are likely to be optimal when the initial data belong to the energy space. On the other hand, for initial data that are smooth and have some decay at infinity, one may ask if precise dispersive time decay rates for the solution in the whole space-time, and not just for {x} in a compact set, may be obtained. The goal of this work is to attack these questions. Our main result gives, for small odd perturbations of the kink that are smooth enough and have some space decay, explicit rates of decay for {a(t)} and for {\psi(t,x)} in the whole space-time domain intersected by a strip {|t| \leq \epsilon^{-4+c}}, for any {c>0}, where {\epsilon} is the size of the initial perturbation. This limitation is due to some new phenomena that appear along lines {x\pm\frac{\sqrt{2}}{3}t} that cannot be detected by a local in space analysis. Our method of proof relies on construction of approximate solutions to the equation satisfied by {\psi}, conjugation of the latter in order to eliminate several potential terms, and normal forms to get rid of problematic contributions in the nonlinearity. We use also Fermis golden rule in order to prove that the {a(t)Y} component decays when time grows. Mathematics bicssc Second-order semilinear hyperbolic equations msc Stability in context of PDEs msc Asymptotic behavior of solutions to PDEs msc Scattering theory for PDEs msc Paradifferential operators as generalizations of partial differential operators in context of PDEs msc Masmoudi aut https://ems.press/doi/10.4171/mems/1 cover image https://content.ems.press/assets/public/images/books/cover-233.png nam a22 5a 4500 10.4171/90 DE-4084 2022-06-29 a fot 00| 0| cr nn mmmmamaa 220629e20220629gw fot 00| 0|eng d 9783985475193 10.4171/90 doi DE-4084 PB bicssc P bicssc Frank edt The Physics and Mathematics of Elliott Lieb. EMS Press 2022 1 online resource (1372 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books These two volumes are dedicated to Elliott Lieb on the occasion of his 90th birthday. They celebrate his fundamental contributions to the fields of mathematics, physics and chemistry. Around 50 chapters give an extensive account of Liebs impact on a very broad range of topics and the resulting subsequent developments. Many contributions are of an expository character and are accessible to a non-expert audience of researchers in mathematics, physics and chemistry. A non-exhaustive list of topics covered includes the problem of stability of matter, quantum many-body systems, density functional theory, topics in statistical mechanics, entropy inequalities and matrix analysis, functional inequalities and sharp constants. Mathematics bicssc Mathematics & science bicssc Laptev edt Lewin edt Seiringer edt https://ems.press/doi/10.4171/90 cover image https://content.ems.press/assets/public/images/books/cover-234.png nam a22 5a 4500 10.4171/90-1 DE-4084 2022-06-29 a fot 00| 0| cr nn mmmmamaa 220629e20220629gw fot 00| 0|eng d 9783985475216 10.4171/90-1 doi DE-4084 PB bicssc Frank edt The Physics and Mathematics of Elliott Lieb. The 90th Anniversary Volume I EMS Press 2022 1 online resource (680 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books These two volumes are dedicated to Elliott Lieb on the occasion of his 90th birthday. They celebrate his fundamental contributions to the fields of mathematics, physics and chemistry. Around 50 chapters give an extensive account of Liebs impact on a very broad range of topics and the resulting subsequent developments. Many contributions are of an expository character and are accessible to a non-expert audience of researchers in mathematics, physics and chemistry. A non-exhaustive list of topics covered includes the problem of stability of matter, quantum many-body systems, density functional theory, topics in statistical mechanics, entropy inequalities and matrix analysis, functional inequalities and sharp constants. Mathematics bicssc Laptev edt Lewin edt Seiringer edt https://ems.press/doi/10.4171/90-1 cover image https://content.ems.press/assets/public/images/books/cover-235.png nam a22 5a 4500 10.4171/90-2 DE-4084 2022-06-29 a fot 00| 0| cr nn mmmmamaa 220629e20220629gw fot 00| 0|eng d 9783985475223 10.4171/90-2 doi DE-4084 PB bicssc Frank edt The Physics and Mathematics of Elliott Lieb. The 90th Anniversary Volume II EMS Press 2022 1 online resource (692 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books These two volumes are dedicated to Elliott Lieb on the occasion of his 90th birthday. They celebrate his fundamental contributions to the fields of mathematics, physics and chemistry. Around 50 chapters give an extensive account of Liebs impact on a very broad range of topics and the resulting subsequent developments. Many contributions are of an expository character and are accessible to a non-expert audience of researchers in mathematics, physics and chemistry. A non-exhaustive list of topics covered includes the problem of stability of matter, quantum many-body systems, density functional theory, topics in statistical mechanics, entropy inequalities and matrix analysis, functional inequalities and sharp constants. Mathematics bicssc Laptev edt Lewin edt Seiringer edt https://ems.press/doi/10.4171/90-2 cover image https://content.ems.press/assets/public/images/books/cover-236.png nam a22 5a 4500 10.4171/zlam/27 DE-4084 2022-07-01 a fot 00| 0| cr nn mmmmamaa 220701e20220701gw fot 00| 0|eng d 9783985475155 10.4171/zlam/27 doi DE-4084 PB bicssc 81Q50 msc 58J51 msc 37D40 msc Anantharaman aut Quantum Ergodicity and Delocalization of Schrödinger Eigenfunctions. EMS Press 2022 1 online resource (140 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 27 2943-4971 Restricted to subscribers. https://ems.press/books This book deals with various topics in quantum chaos, starting with a historical introduction and then focussing on the delocalisation of eigenfunctions of Schrödinger operators for chaotic Hamiltonian systems. It contains a short introduction to microlocal analysis, necessary for proving the Shnirelman theorem and giving an account of the authors work on entropy of eigenfunctions on negatively curved manifolds. In addition, further work by the author on quantum ergodicity of eigenfunctions on large graphs is presented, along with a survey of results on eigenfunctions on the round sphere, as well as a rather detailed exposition of the result by Backhausz and Szegedy on the Gaussian distribution of eigenfunctions on random regular graphs. Like the lecture series it is based on, the text is aimed at all mathematicians, from the graduate level onwards, who want to learn some of the important ideas in the field. Mathematics bicssc Quantum chaos msc Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity msc Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) msc https://ems.press/doi/10.4171/zlam/27 cover image https://content.ems.press/assets/public/images/books/cover-237.png nam a22 5a 4500 10.4171/zlam/29 DE-4084 2022-12-06 a fot 00| 0| cr nn mmmmamaa 221206e20221206gw fot 00| 0|eng d 9783985475261 10.4171/zlam/29 doi DE-4084 PB bicssc 18-02 msc 18G70 msc 14A22 msc 14H10 msc 16E35 msc 16E45 msc Polishchuk aut A-Structures and Moduli Spaces. EMS Press 2022 1 online resource (178 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 29 2943-4971 Restricted to subscribers. https://ems.press/books This book discusses certain moduli problems related to A-structures. These structures can be viewed as a way of recording extra information on cohomology algebras. They are useful in describing derived categories appearing in geometry, and as such, they play an important role in homological mirror symmetry. The author presents some general results on the classification of A-structures. For example, he gives a sufficient criterion for the existence of a finite-type moduli scheme of A-structures extending a given associative algebra. He also considers two concrete moduli problems for A-structures. The first is related to the moduli spaces of curves, while the second is related to the classification of solutions of an associative version of the Yang-Baxter equation. The book will be of interest to graduate students and researchers working in homological algebra, algebraic geometry, and related areas. Mathematics bicssc Research exposition (monographs, survey articles) pertaining to category theory msc \(A_{\infty}\)-categories, relations with homological mirror symmetry msc Noncommutative algebraic geometry msc Families, moduli of curves (algebraic) msc Derived categories and associative algebras msc Differential graded algebras and applications (associative algebraic aspects) msc https://ems.press/doi/10.4171/zlam/29 cover image https://content.ems.press/assets/public/images/books/cover-240.png nam a22 5a 4500 10.4171/hem/13 DE-4084 2023-05-04 a fot 00| 0| cr nn mmmmamaa 230504e20230504gw fot 00| 0|eng d 9783985475117 10.4171/hem/13 doi DE-4084 PB bicssc 01A55 msc 01A60 msc 01A75 msc 11E25 msc 11R52 msc 13G05 msc 16-03 msc 17A75 msc Steuding aut Hurwitzs Lectures on the Number Theory of Quaternions. EMS Press 2023 1 online resource (311 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 13 2523-5222 Restricted to subscribers. https://ems.press/books Quaternions are non-commutative generalizations of the complex numbers, invented by William Rowan Hamilton in 1843. Their number-theoretical aspects were first investigated by Rudolf Lipschitz in the 1880s, and, in a streamlined form, by Adolf Hurwitz in 1896. This book contains an English translation of his 1919 textbook on this topic as well as his famous 1-2-3-4 theorem on composition algebras. In addition, the reader can find commentaries that shed historical light on the development of this number theory of quaternions, for example, the classical preparatory works (of Fermat, Euler, Lagrange and Gauss to name but a few), the different notions of quaternion integers in the works of Lipschitz and Hurwitz, analogies to the theory of algebraic numbers, and the further development (including Dicksons work in particular). The authors have implemented parts of the book in stand-alone courses, and they further believe that the present book can also complement well a course on algebraic number theory (with respect to a non-commutative extension of the rational numbers). Mathematics bicssc History of mathematics in the 19th century msc History of mathematics in the 20th century msc Collected or selected works; reprintings or translations of classics msc Sums of squares and representations by other particular quadratic forms msc Quaternion and other division algebras: arithmetic, zeta functions msc Integral domains msc History of associative rings and algebras msc Composition algebras msc Oswald aut https://ems.press/doi/10.4171/hem/13 cover image https://content.ems.press/assets/public/images/books/cover-257.png nam a22 5a 4500 10.4171/mems/2 DE-4084 2022-12-08 a fot 00| 0| cr nn mmmmamaa 221208e20221208gw fot 00| 0|eng d 9783985475230 10.4171/mems/2 doi DE-4084 PB bicssc 53D45 msc 14N35 msc 18G80 msc Cotti aut Cyclic Stratum of Frobenius Manifolds, Borel-Laplace (, )-Multitransforms, and Integral Representations of Solutions of Quantum Differential Equations. EMS Press 2022 1 online resource (134 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 2 2747-9099 Open Access https://ems.press/books In the first part of this paper, we introduce the notion of *cyclic stratum* of a Frobenius manifold \smash{M}. This is the set of points of the extended manifold \smash{\mathbb C^*\times M} at which the unit vector field is a cyclic vector for the isomonodromic system defined by the flatness condition of the extended deformed connection. The study of the geometry of the complement of the cyclic stratum is addressed. We show that at points of the cyclic stratum, the isomonodromic system attached to \smash{M} can be reduced to a scalar differential equation, called the *master differential equation* of \smash{M}. In the case of Frobenius manifolds coming from Gromov-Witten theory, namely quantum cohomologies of smooth projective varieties, such a construction reproduces the notion of quantum differential equation. In the second part of the paper, we introduce two multilinear transforms, called *Borel-Laplace* (\boldsymbol{\alpha}, \boldsymbol{\beta})-*multitransforms*, on spaces of Ribenboim formal power series with exponents and coefficients in an arbitrary finite-dimensional \smash{\mathbb C}-algebra \smash{A}. When \smash{A} is specialized to the cohomology of smooth projective varieties, the integral forms of the *Borel-Laplace* (\boldsymbol{\alpha}, \boldsymbol{\beta})-multitransforms are used in order to rephrase the Quantum Lefschetz theorem. This leads to explicit Mellin-Barnes integral representations of solutions of the quantum differential equations for a wide class of smooth projective varieties, including Fano complete intersections in projective spaces. In the third and final part of the paper, as an application, we show how to use the new analytic tools, introduced in the previous parts, in order to study the quantum differential equations of Hirzebruch surfaces. For Hirzebruch surfaces diffeomorphic to \smash{\mathbb P^1\times \mathbb P^1}, this analysis reduces to the simpler quantum differential equation of \smash{\mathbb P^1}. For Hirzebruch surfaces diffeomorphic to the blow-up of \smash{\mathbb P^2} in one point, the quantum differential equation is integrated via Laplace \smash{(1,2;\frac{1}{2},\frac{1}{3})}-multitransforms of solutions of the quantum differential equations of \smash{\mathbb P^1} and \smash{\mathbb P^2}, respectively. This leads to explicit integral representations for the Stokes bases of solutions of the quantum differential equations, and finally to the proof of the Dubrovin conjecture for all Hirzebruch surfaces. Mathematics bicssc Gromov-Witten invariants, quantum cohomology, Frobenius manifolds msc Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) msc Derived categories, triangulated categories msc https://ems.press/doi/10.4171/mems/2 cover image https://content.ems.press/assets/public/images/books/cover-241.png nam a22 5a 4500 10.4171/8ecm DE-4084 2023-07-14 a fot 10| 0| cr nn mmmmamaa 230714e20230714gw fot 10| 0|eng d 9783985475513 10.4171/8ecm doi DE-4084 PB bicssc 00B25 msc Hujdurović edt European Congress of Mathematics ; Portorož, 20-26 June, 2021. EMS Press 2023 1 online resource (982 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Open Access https://ems.press/books The European Congress of Mathematics, held every four years, is a well-established major international mathematical event. Following those in Paris (1992), Budapest (1996), Barcelona (2000), Stockholm (2004), Amsterdam (2008), Kraków (2012), and Berlin (2016), the Eighth European Congress of Mathematics (8ECM) took place in Portorož, Slovenia, June 20-26, 2021, with about 1700 participants from all over the world, mostly online due to Covid pandemic. Ten plenary and thirty invited lectures along with the special Abel and Hirzebruch lectures formed the core of the program. As in all the previous EMS congresses, ten outstanding young mathematicians received the EMS prizes in recognition of their research achievements. In addition, two more prizes were awarded: The Felix Klein Prize for a remarkable solution of an industrial problem and the Otto Neugebauer Prize for a highly original and influential piece of work in the history of mathematics. The program was complemented by five public lectures, several exhibitions, and 62 minisymposia with about 1000 contributions, spread over all areas of mathematics. A number of panel discussions and meetings were organized, covering a variety of issues ranging from the future of mathematical publishing and the role of the ERC to public awareness of mathematics. These proceedings provide a permanent record of current mathematics of highest quality by presenting extended versions of seven plenary, six prize, and fourteen invited lectures as well as eleven lectures from minisymposia keynote speakers, all of which were delivered during the congress. Mathematics bicssc Proceedings of conferences of miscellaneous specific interest msc Kutnar edt Marušič edt Miklavič edt Pisanski edt Šparl edt https://ems.press/doi/10.4171/8ecm cover image https://content.ems.press/assets/public/images/books/cover-262.png nam a22 5a 4500 10.4171/etb/24 DE-4084 2022-12-20 a fot 00| 0| cr nn mmmmamaa 221220e20221220gw fot 00| 0|eng d 9783985475179 10.4171/etb/24 doi DE-4084 PB bicssc 05-01 msc 05Cxx msc 08Axx msc 20-XX msc 54-XX msc Bretto aut Elements of Graph Theory ; From Basic Concepts to Modern Developments. EMS Press 2022 1 online resource (502 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 24 2943-4955 Restricted to subscribers. https://ems.press/books This book is an introduction to graph theory, presenting most of its elementary and classical notions through an original and rigorous approach, including detailed proofs of most of the results. It covers all aspects of graph theory from an algebraic, topological and analytic point of view, while also developing the theorys algorithmic parts. The variety of topics covered aims to lead the reader in understanding graphs in their greatest diversity in order to perceive their power as a mathematical tool. The book will be useful to undergraduate students in computer science and mathematics as well as in engineering, but it is also intended for graduate students. It will also be of use to both early-stage and experienced researchers wanting to learn more about graphs. Mathematics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics msc Graph theory msc Algebraic structures msc Group theory and generalizations msc General topology msc Faisant aut Hennecart aut https://ems.press/doi/10.4171/etb/24 cover image https://content.ems.press/assets/public/images/books/cover-243.png nam a22 5a 4500 10.4171/etb/26 DE-4084 2023-07-27 a fot 00| 0| cr nn mmmmamaa 230727e20230727gw fot 00| 0|eng d 9783985475186 10.4171/etb/26 doi DE-4084 PB bicssc 51-01 msc 51F99 msc 20F69 msc 19K56 msc 57-01 msc 46L87 msc 58B34 msc 46L99 msc 53C20 msc Nowak aut Large Scale Geometry ; Second Edition. EMS Press 2023 1 online resource (213 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 26 2943-4955 Restricted to subscribers. https://ems.press/books Large scale geometry is the study of geometric objects viewed from a great distance. The idea of large scale geometry can be traced back to Mostows work on rigidity and the work of Švarc, Milnor and Wolf on growth of groups and is greatly influenced by Gromovs work on geometric group theory. In the last decades, large scale geometry has found important applications in group theory, topology, geometry, higher index theory, computer science, and large data analysis. This book provides a friendly approach to the basic theory of this exciting and fast growing subject and offers a glimpse of its applications to topology, geometry, and higher index theory. The authors have made a conscientious effort to make the book accessible to advanced undergraduate students, graduate students, and non-experts. The present second edition has been updated to cover recent developments involving constructions of groups and metric spaces with exotic properties as well as results charting new directions in index theory, and it also includes minor improvements in the presentation and an updated bibliography. For the first edition of this book, please click [here](https://doi.org/10.4171/112). Mathematics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry msc Metric geometry msc Asymptotic properties of groups msc Index theory msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes msc Noncommutative differential geometry msc Noncommutative geometry (à la Connes) msc Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.) msc Global Riemannian geometry, including pinching msc Yu aut https://ems.press/doi/10.4171/etb/26 cover image https://content.ems.press/assets/public/images/books/cover-264.png nam a22 5a 4500 10.4171/st/17 DE-4084 2022-12-21 a fot 00| 0| cr nn mmmmamaa 221221e20221221gw fot 00| 0|eng d 9783985475131 10.4171/st/17 doi DE-4084 PB bicssc 01A70 msc 01A55 msc 01A60 msc 01A80 msc Guiraldenq aut Émile Borel ; A Life in Mathematics and Politics Across Two Centuries. EMS Press 2022 1 online resource (122 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books Emile Borel, one of the early developers of measure theory and probability, was among the first to show the importance of the calculus of probability as a tool for the experimental sciences. A prolific and gifted researcher, his scientific works, so vast in number and scope, earned him international recognition. In addition, at the origin of the foundation of the Institut Henri Poincare in Paris and longtime its director, he also served as member of the French Parliament, minister of the Navy, president of the League of Nations Union, and president of the French Academy of Sciences. The book follows Borel, one of Frances leading scientific and political figures of the first half of the twentieth century, through the various stages and the most significant events of his life, across two centuries and two wars. Originally published in French, this new English edition of the book will appeal primarily to mathematicians and those with an interest in the history of science, but it should not disappoint anyone wishing to explore, through the life of an exceptional scientist and man, a chapter of history from the Franco-Prussian War of 1870 to the beginnings of contemporary Europe. Mathematics bicssc Biographies, obituaries, personalia, bibliographies msc History of mathematics in the 19th century msc History of mathematics in the 20th century msc Sociology (and profession) of mathematics msc https://ems.press/doi/10.4171/st/17 cover image https://content.ems.press/assets/public/images/books/cover-244.png nam a22 5a 4500 10.4171/etb/28 DE-4084 2024-09-07 a fot 00| 0| cr nn mmmmamaa 240907e20240907gw fot 00| 0|eng d 9783985475162 10.4171/etb/28 doi DE-4084 PB bicssc 34-01 msc 65-01 msc 34A09 msc 34A30 msc 34A36 msc 34D20 msc 34D30 msc 34B05 msc 34B15 msc 65L80 msc 65L10 msc 65L20 msc 65L06 msc 65L07 msc Kunkel aut Differential-Algebraic Equations ; Analysis and Numerical Solution. EMS Press 2024 1 online resource (538 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 28 2943-4955 Restricted to subscribers. https://ems.press/books Differential-algebraic equations are a widely accepted tool for the modeling and simulation of constrained dynamical systems in numerous applications, such as mechanical multibody systems, electrical circuit simulation, chemical engineering, control theory, fluid dynamics and many other areas. In the second edition of this textbook a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations is provided. The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear systems. Further sections on control problems, optimal control, stability theory, generalized inverses of differential-algebraic operators, generalized solutions, differential equations on manifolds, and differential-algebraic equations with symmetries complement the theoretical treatment of initial value problems. Two major classes of numerical methods for differential-algebraic equations (Runge-Kutta and BDF methods) are discussed and analyzed with respect to convergence and order. A chapter is devoted to index reduction methods that allow the numerical treatment of general differential-algebraic equations. The analysis and numerical solution of boundary value problems for differential-algebraic equations is presented, including multiple shooting and collocation methods. A chapter on further selected topics dealing with overdetermined consistent systems, root finding, pathfollowing, hybrid systems, and dissipative Hamiltonian systems completes the book. A prerequisite for the reader is the standard course on the theory and numerical solution of ordinary differential equations. Numerous examples and exercises make the book suitable as a course textbook or for self-study. Mathematics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis msc Implicit ordinary differential equations, differential-algebraic equations msc Linear ordinary differential equations and systems msc Discontinuous ordinary differential equations msc Stability of solutions to ordinary differential equations msc Structural stability and analogous concepts of solutions to ordinary differential equations msc Linear boundary value problems for ordinary differential equations msc Nonlinear boundary value problems for ordinary differential equations msc Numerical methods for differential-algebraic equations msc Numerical solution of boundary value problems involving ordinary differential equations msc Stability and convergence of numerical methods for ordinary differential equations msc Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations msc Numerical investigation of stability of solutions to ordinary differential equations msc Mehrmann aut https://ems.press/doi/10.4171/etb/28 cover image https://content.ems.press/assets/public/images/books/cover-294.png nam a22 5a 4500 10.4171/mems/4 DE-4084 2023-06-08 a fot 00| 0| cr nn mmmmamaa 230608e20230608gw fot 00| 0|eng d 9783985475490 10.4171/mems/4 doi DE-4084 PB bicssc 35P25 msc 35Q40 msc 81Q10 msc 47A10 msc 47A40 msc Sukochev aut The Limiting Absorption Principle for Massless Dirac Operators, Properties of Spectral Shift Functions, and an Application to the Witten Index of Non-Fredholm Operators. EMS Press 2023 1 online resource (213 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 4 2747-9099 Open Access https://ems.press/books Applying the theory of strongly smooth operators, we derive a limiting absorption principle (LAP) on any compact interval on the real line away from zero for the *n*-dimensional free massless Dirac operator *H*, and then use this to demonstrate the absence of singular continuous spectrum of interacting massless Dirac operators *H* *H* + *V*, where the entries of the (essentially bounded) matrix-valued potential *V* decay appropriately at spatial infinity. This includes the special case of electromagnetic potentials. In addition, we derive a one-to-one correspondence between embedded eigenvalues of *H* (away from zero) and the eigenvalue 1 of an underlying Birman-Schwinger-type operator. In addition, expressing the spectral shift function for the pair (*H*,*H*) as normal boundary values of associated regularized Fredholm determinants to the real axis, we then prove that under appropriate additional decay hypotheses on *V*, the spectral shift function for (*H*,*H*) is continuous away from zero and that its left and right limits at zero exist. This fact is then used to express the resolvent regularized Witten index of the non-Fredholm operator *D*_*A* (*d*/*dt*) + *A*, where *A* represents the direct integral over a family operators *A*(*t*) that has asymptotes *A* and *A* as *t* tends to + infinity and infinity (in the norm resolvent sense), respectively, in terms of the spectral shift function for the pair (*H*,*H*). Mathematics bicssc Scattering theory for PDEs msc PDEs in connection with quantum mechanics msc Selfadjoint operator theory in quantum theory, including spectral analysis msc Spectrum, resolvent msc Scattering theory of linear operators msc Carey aut Gesztesy aut Levitina aut Nichols aut Zanin aut https://ems.press/doi/10.4171/mems/4 cover image https://content.ems.press/assets/public/images/books/cover-259.png nam a22 5a 4500 10.4171/zlam/28 DE-4084 2022-12-06 a fot 00| 0| cr nn mmmmamaa 221206e20221206gw fot 00| 0|eng d 9783985475285 10.4171/zlam/28 doi DE-4084 PB bicssc 35J15 msc 35B65 msc 35J05 msc 35J20 msc 35J60 msc 35R35 msc Fernández-Real aut Regularity Theory for Elliptic PDE. EMS Press 2022 1 online resource (236 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 28 2943-4971 Restricted to subscribers. https://ems.press/books One of the most basic mathematical questions in PDE is that of regularity. A classical example is Hilberts XIXth problem, stated in 1900, which was solved by De Giorgi and Nash in the 1950s. The question of regularity has been a central line of research in elliptic PDE during the second half of the 20th century and has influenced many areas of mathematics linked one way or another with PDE. This text aims to provide a self-contained introduction to the regularity theory for elliptic PDE, focusing on the main ideas rather than proving all results in their greatest generality. It can be seen as a bridge between an elementary PDE course and more advanced books. The book starts with a short review of the Laplace operator and harmonic functions. The theory of Schauder estimates is developed next, but presented with various proofs of the results. Nonlinear elliptic PDE are covered in the following, both in the variational and non-variational setting and, finally, the obstacle problem is studied in detail, establishing the regularity of solutions and free boundaries. Mathematics bicssc Second-order elliptic equations msc Smoothness and regularity of solutions to PDEs msc Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation msc Variational methods for second-order elliptic equations msc Nonlinear elliptic equations msc Free boundary problems for PDEs msc Ros-Oton aut https://ems.press/doi/10.4171/zlam/28 cover image https://content.ems.press/assets/public/images/books/cover-239.png nam a22 5a 4500 10.4171/etm/35 DE-4084 2023-08-21 a fot 00| 0| cr nn mmmmamaa 230821e20230821gw fot 00| 0|eng d 9783985475391 10.4171/etm/35 doi DE-4084 PB bicssc 51E24 msc 20E42 msc 20F55 msc 51F15 msc 51-02 msc Rousseau aut Euclidean Buildings ; Geometry and Group Actions. EMS Press 2023 1 online resource (607 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 35 2943-5005 Restricted to subscribers. https://ems.press/books The theory of buildings lies at the interplay between geometry and group theory, and is one of the main tools for studying the structure of many groups. Actually, buildings were introduced by Jacques Tits in the 1950s to better understand and study a semi-simple algebraic group over a field. For a general field, its associated building is a spherical building, called its Tits building. It is a simplicial complex and, in this book, one considers a geometric realization called vectorial building. When the field is real valued, François Bruhat and Jacques Tits constructed another building taking into account the topology of the field. This Bruhat-Tits building is a polysimplicial complex and its usual geometric realization is an affine building. These vectorial or affine buildings are the main examples of Euclidean buildings. The present book develops the general abstract theory of these Euclidean buildings (the buildings with Euclidean affine spaces as apartments). It is largely self-contained and emphasizes the metric aspects of these objects, as CAT(0) spaces very similar to Riemannian symmetric spaces of non-compact type. The book studies their compactifications, their links with groups, many classical examples, and some applications (for example, to Hecke algebras). Mathematics bicssc Buildings and the geometry of diagrams msc Groups with a \(BN\)-pair; buildings msc Reflection and Coxeter groups (group-theoretic aspects) msc Reflection groups, reflection geometries msc Research exposition (monographs, survey articles) pertaining to geometry msc https://ems.press/doi/10.4171/etm/35 cover image https://content.ems.press/assets/public/images/books/cover-267.png nam a22 5a 4500 10.4171/esiam/3 DE-4084 2022-12-12 a fot 00| 0| cr nn mmmmamaa 221212e20221212gw fot 00| 0|eng d 9783985475278 10.4171/esiam/3 doi DE-4084 PB bicssc 35-02 msc 76D05 msc 74B20 msc Garrione edt Interactions between Elasticity and Fluid Mechanics. EMS Press 2022 1 online resource (248 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series in Industrial and Applied Mathematics (esiam) 3 2523-5095 Restricted to subscribers. https://ems.press/books Partial differential equations arise naturally in mathematical physics and have numerous applications in real life. The present book mainly focuses on fluid mechanics, elasticity, and their interactions. As a typical model of such phenomena, one may consider the fluid-structure interactions between the wind and a suspension bridge. Not much is known about the mechanisms generating instabilities (in a broad sense) and many problems are still open, while an interdisciplinary approach is necessary for a better understanding of all the involved phenomena. This book collects different points of view on these phenomena and is addressed both to junior researchers entering the field as well as to experienced professionals aiming to expand their scientific knowledge to closely related disciplines. The book also aims to bring closer the mathematical and engineering communities in order to create a common language and to encourage future collaborations. Mathematics bicssc Research exposition (monographs, survey articles) pertaining to partial differential equations msc Navier-Stokes equations for incompressible viscous fluids msc Nonlinear elasticity msc Gazzola edt https://ems.press/doi/10.4171/esiam/3 cover image https://content.ems.press/assets/public/images/books/cover-242.png nam a22 5a 4500 10.4171/esi/11 DE-4084 2023-07-26 a fot 00| 0| cr nn mmmmamaa 230726e20230726gw fot 00| 0|eng d 9783985475292 10.4171/esi/11 doi DE-4084 PB bicssc 76-02 msc 86-02 msc 76D05 msc 76D33 msc 76M45 msc 76N06 msc 76N30 msc 76U60 msc 86A05 msc 86A10 msc Johnson aut An Introduction to the Mathematical Fluid Dynamics of Oceanic and Atmospheric Flows. EMS Press 2023 1 online resource (176 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda ESI Lectures in Mathematics and Physics (esi) 11 2943-4939 Restricted to subscribers. https://ems.press/books The study of the movement of the atmosphere and the oceans is intriguing, challenging and important, particularly in the context of current concerns about the climate. The familiar and tested approach to these problems is based on the construction of model equations, tailored to address specific flow scenarios. In this text, we present a single, over-arching approach which uses the thin-shell approximation - and nothing more - applied to the general equations of fluid dynamics. This allows a range of classical problems, and some new applications, to be accessed from a single formulation which retains all the relevant physical attributes, as well as the essential characteristics of the spherical geometry. The approximations and assumptions are clear and higher-order terms are readily accessible. The main aim is to present the material in a mathematically consistent and robust fashion - in the applied sense - emphasising the systematic, asymptotic methods usually employed in mathematical fluid dynamics. This is not a textbook that introduces the physical principles underpinning the study of the oceans and the atmosphere. Rather, it is intended to enhance the more usual modelling approach to these studies and, more significantly, to introduce those with mathematical interests, but no expertise in these particular applications, to these types of problems. The text is suitable for researchers, and students, in the oceanic and atmospheric sciences, and for mathematicians - again researchers and students - with an interest in the application of fluid dynamics to more complicated flow scenarios. Mathematics bicssc Research exposition (monographs, survey articles) pertaining to fluid mechanics msc Research exposition (monographs, survey articles) pertaining to geophysics msc Navier-Stokes equations for incompressible viscous fluids msc Waves for incompressible viscous fluids msc Asymptotic methods, singular perturbations applied to problems in fluid mechanics msc Compressible Navier-Stokes equations msc Waves in compressible fluids msc Geophysical flows msc Hydrology, hydrography, oceanography msc Meteorology and atmospheric physics msc https://ems.press/doi/10.4171/esi/11 cover image https://content.ems.press/assets/public/images/books/cover-263.png nam a22 5a 4500 10.4171/mems/3 DE-4084 2023-04-27 a fot 00| 0| cr nn mmmmamaa 230427e20230427gw fot 00| 0|eng d 9783985475254 10.4171/mems/3 doi DE-4084 PB bicssc 05C63 msc 05C90 msc 34B45 msc 35R02 msc 60J27 msc 81Q35 msc Kostenko aut Laplacians on Infinite Graphs. EMS Press 2023 1 online resource (240 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 3 2747-9099 Open Access https://ems.press/books The main focus in this memoir is on Laplacians on both weighted graphs and weighted metric graphs. Let us emphasize that we consider infinite locally finite graphs and do not make any further geometric assumptions. Whereas the existing literature usually treats these two types of Laplacian operators separately, we approach them in a uniform manner in the present work and put particular emphasis on the relationship between them. One of our main conceptual messages is that these two settings should be regarded as complementary (rather than opposite) and exactly their interplay leads to important further insight on both sides. Our central goal is twofold. First of all, we explore the relationships between these two objects by comparing their basic spectral (self-adjointness, spectral gap, etc.), parabolic (Markovian uniqueness, recurrence, stochastic completeness, etc.), and metric (quasi isometries, intrinsic metrics, etc.) properties. In turn, we exploit these connections either to prove new results for Laplacians on metric graphs or to provide new proofs and perspective on the recent progress in weighted graph Laplacians. We also demonstrate our findings by considering several important classes of graphs (Cayley graphs, tessellations, and antitrees). Mathematics bicssc Infinite graphs msc Applications of graph theory msc Boundary value problems on graphs and networks for ordinary differential equations msc PDEs on graphs and networks (ramified or polygonal spaces) msc Continuous-time Markov processes on discrete state spaces msc Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices msc Nicolussi aut https://ems.press/doi/10.4171/mems/3 cover image https://content.ems.press/assets/public/images/books/cover-256.png nam a22 5a 4500 10.4171/dms/1 DE-4084 1998-01-01 a fot 10| 0| cr nn mmmmamaa 980101e19980101gw fot 10| 0|eng d 9783985475438 10.4171/dms/1 doi DE-4084 PB bicssc 00B25 msc Rehmann edt Proceedings of the International Congress of Mathematicians 1998 ; Berlin, Germany, 18-27 August 1998. EMS Press 1998 1 online resource (2195 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Documenta Mathematica Series (dms) 1 2943-4998 Free to read https://ems.press/books The Proceedings of the International Congress of Mathematicians 1998, held in Berlin, are published - electronically and in print - in three volumes. Volume I contains information on the organization of the Congress including the list of participants, reports on the opening and closing ceremonies, the Laudationes on the Fields Medalists and the Nevanlinna Prize Winner, and the Plenary Lectures. Volumes II and III contain the Invited Lectures. Mathematics bicssc Proceedings of conferences of miscellaneous specific interest msc Fischer edt https://ems.press/doi/10.4171/dms/1 cover image https://content.ems.press/assets/public/images/books/cover-245.png nam a22 5a 4500 10.4171/dms/1-1 DE-4084 1998-01-01 a fot 10| 0| cr nn mmmmamaa 980101e19980101gw fot 10| 0|eng d 9783985475445 10.4171/dms/1-1 doi DE-4084 PB bicssc 00B25 msc Rehmann edt Proceedings of the International Congress of Mathematicians 1998. Volume I. Plenary Lectures and Ceremonies EMS Press 1998 1 online resource (662 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Documenta Mathematica Series (dms) 1 2943-4998 Free to read https://ems.press/books The Proceedings of the International Congress of Mathematicians 1998, held in Berlin, are published - electronically and in print - in three volumes. Volume I contains information on the organization of the Congress including the list of participants, reports on the opening and closing ceremonies, the Laudationes on the Fields Medalists and the Nevanlinna Prize Winner, and the Plenary Lectures. Volumes II and III contain the Invited Lectures. Mathematics bicssc Proceedings of conferences of miscellaneous specific interest msc Fischer edt https://ems.press/doi/10.4171/dms/1-1 cover image https://content.ems.press/assets/public/images/books/cover-246.png nam a22 5a 4500 10.4171/dms/1-2 DE-4084 1998-01-01 a fot 10| 0| cr nn mmmmamaa 980101e19980101gw fot 10| 0|eng d 9783985475452 10.4171/dms/1-2 doi DE-4084 PB bicssc 00B25 msc Fischer edt Proceedings of the International Congress of Mathematicians 1998. Volume II. Invited Lectures EMS Press 1998 1 online resource (881 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Documenta Mathematica Series (dms) 1 2943-4998 Free to read https://ems.press/books The Proceedings of the International Congress of Mathematicians 1998, held in Berlin, are published - electronically and in print - in three volumes. Volume I contains information on the organization of the Congress including the list of participants, reports on the opening and closing ceremonies, the Laudationes on the Fields Medalists and the Nevanlinna Prize Winner, and the Plenary Lectures. Volumes II and III contain the Invited Lectures. Mathematics bicssc Proceedings of conferences of miscellaneous specific interest msc Rehmann edt https://ems.press/doi/10.4171/dms/1-2 cover image https://content.ems.press/assets/public/images/books/cover-247.png nam a22 5a 4500 10.4171/dms/1-3 DE-4084 1998-01-01 a fot 10| 0| cr nn mmmmamaa 980101e19980101gw fot 10| 0|eng d 9783985475469 10.4171/dms/1-3 doi DE-4084 PB bicssc 00B25 msc Rehmann edt Proceedings of the International Congress of Mathematicians 1998. Volume III. Invited Lectures EMS Press 1998 1 online resource (825 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Documenta Mathematica Series (dms) 1 2943-4998 Free to read https://ems.press/books The Proceedings of the International Congress of Mathematicians 1998, held in Berlin, are published - electronically and in print - in three volumes. Volume I contains information on the organization of the Congress including the list of participants, reports on the opening and closing ceremonies, the Laudationes on the Fields Medalists and the Nevanlinna Prize Winner, and the Plenary Lectures. Volumes II and III contain the Invited Lectures. Mathematics bicssc Proceedings of conferences of miscellaneous specific interest msc Fischer edt https://ems.press/doi/10.4171/dms/1-3 cover image https://content.ems.press/assets/public/images/books/cover-248.png nam a22 5a 4500 10.4171/dms/2 DE-4084 2001-01-01 a fot 10| 0| cr nn mmmmamaa 010101e20010101gw fot 10| 0|eng d 9783985475421 10.4171/dms/2 doi DE-4084 PB bicssc Hoffman edt Proceedings of the Conference on Quadratic Forms and Related Topics ; Baton Rouge, Louisiana, USA, 26-30 March 2001. EMS Press 2001 1 online resource (241 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Documenta Mathematica Series (dms) 2 2943-4998 Free to read https://ems.press/books Mathematics bicssc Hurrelbrink edt Morales edt Perlis edt van Wamelen edt https://ems.press/doi/10.4171/dms/2 cover image https://content.ems.press/assets/public/images/books/cover-249.png nam a22 5a 4500 10.4171/dms/3 DE-4084 2003-01-01 a fot 00| 0| cr nn mmmmamaa 030101e20030101gw fot 00| 0|eng d 9783985475476 10.4171/dms/3 doi DE-4084 PB bicssc 00B30 msc 01A70 msc Bloch edt A Collection of Manuscripts Written in Honour of Kazuya Kato on the Occasion of His Fiftieth Birthday. EMS Press 2003 1 online resource (914 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Documenta Mathematica Series (dms) 3 2943-4998 Free to read https://ems.press/books Mathematics bicssc Festschriften msc Biographies, obituaries, personalia, bibliographies msc Fesenko edt Illusie edt Kurihara edt Saito edt Saito edt Schneider edt https://ems.press/doi/10.4171/dms/3 cover image https://content.ems.press/assets/public/images/books/cover-250.png nam a22 5a 4500 10.4171/dms/4 DE-4084 2006-01-01 a fot 00| 0| cr nn mmmmamaa 060101e20060101gw fot 00| 0|eng d 9783985475414 10.4171/dms/4 doi DE-4084 PB bicssc PB bicssc 00B30 msc 11-06 msc 14-06 msc Fesenko edt A Collection of Manuscripts Written in Honour of John H. Coates on the Occasion of His Sixtieth Birthday. EMS Press 2006 1 online resource (821 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Documenta Mathematica Series (dms) 4 2943-4998 Free to read https://ems.press/books This volume is dedicated to Professor John H. Coates, an outstanding contributor to number theory, both through his pioneering and fundamental mathematical works and through the magnificent mathematical school he has established. It contains 24 articles written by 38 authors on a wide range of topics in the cutting edge of research in number theory, algebraic geometry and analysis: zeta functions and L-functions, automorphic and modularity issues, Galois representations,arithmetic of elliptic curves, Iwasawa theory, noncommutative Iwasawa theory, and p-adic analysis. Mathematics bicssc Mathematics bicssc Festschriften msc Proceedings, conferences, collections, etc. pertaining to number theory msc Proceedings, conferences, collections, etc. pertaining to algebraic geometry msc Lichtenbaum edt Perrin-Riou edt Schneider edt https://ems.press/doi/10.4171/dms/4 cover image https://content.ems.press/assets/public/images/books/cover-254.png nam a22 5a 4500 10.4171/dms/5 DE-4084 2010-01-01 a fot 00| 0| cr nn mmmmamaa 100101e20100101gw fot 00| 0|eng d 9783985470419 10.4171/dms/5 doi DE-4084 PB bicssc PB bicssc 00B30 msc 11-06 msc 14-06 msc 20-06 msc Fesenko edt A Collection of Manuscripts Written in Honour of Andrei A. Suslin on the Occasion of His Sixtieth Birthday. EMS Press 2010 1 online resource (719 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Documenta Mathematica Series (dms) 5 2943-4998 Free to read https://ems.press/books Over four decades, Andrei Suslin has conducted inspirational research at St. Petersburg University (LOMI) and Northwestern University. Andreis impact on algebraic K-theory, motivic cohomology, central simple algebras, cohomology of groups, and representation theory have fundamentally changed these subjects. Many of the best results in these areas are due to Andrei, many more were achieved using his ideas and guidance. Andreis influence extends beyond his published achievements, for he has been most generous in sharing his ideas and insights. With great admiration, this volume of Documenta Mathematica is dedicated to him. Mathematics bicssc Mathematics bicssc Festschriften msc Proceedings, conferences, collections, etc. pertaining to number theory msc Proceedings, conferences, collections, etc. pertaining to algebraic geometry msc Proceedings, conferences, collections, etc. pertaining to group theory msc Friedlander edt Merkurjev edt Rehmann edt https://ems.press/doi/10.4171/dms/5 cover image https://content.ems.press/assets/public/images/books/cover-255.png nam a22 5a 4500 10.4171/dms/6 DE-4084 2012-01-01 a fot 00| 0| cr nn mmmmamaa 120101e20120101gw fot 00| 0|eng d 9783985475407 10.4171/dms/6 doi DE-4084 PB bicssc PB bicssc 00B25 msc 90-06 msc 90Cxx msc Grötschel edt Optimization Stories ; 21st International Symposium on Mathematical Programming. Berlin, Germany, 19-24 August 2012. EMS Press 2012 1 online resource (460 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Documenta Mathematica Series (dms) 6 2943-4998 Free to read https://ems.press/books Mathematics bicssc Mathematics bicssc Proceedings of conferences of miscellaneous specific interest msc Proceedings, conferences, collections, etc. pertaining to operations research and mathematical programming msc Mathematical programming msc https://ems.press/doi/10.4171/dms/6 cover image https://content.ems.press/assets/public/images/books/cover-251.png nam a22 5a 4500 10.4171/dms/7 DE-4084 2015-01-01 a fot 00| 0| cr nn mmmmamaa 150101e20150101gw fot 00| 0|eng d 9783985470402 10.4171/dms/7 doi DE-4084 PB bicssc 00B30 msc 01A70 msc Balmer edt A Collection of Manuscripts Written in Honour of Alexander S. Merkurjev on the Occasion of His Sixtieth Birthday. EMS Press 2015 1 online resource (588 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Documenta Mathematica Series (dms) 7 2943-4998 Free to read https://ems.press/books This volume is dedicated to Professor Alexander S. Merkurjev, one of the worlds leading algebraists, in recognition of his fundamental contributions to algebraic K-theory, quadratic forms, Galois cohomology, algebraic groups, essential dimension, aspects of arithmetic and algebraic geometry. 23 papers in the volume advance topics in local commutative algebra, homogeneous varieties, homology classes for varieties over finite fields, birational geometry, coordinates in polynomial rings over algebraically closed fields, hermitian lattices, bundles over surfaces, characteristic classes, semisimple groups, cohomological invariants, algebras with involution, algebraic K-theory, oriented cohomology of flag varieties, cycles on algebraic varieties, mixed motives, motivic stable homotopy, p-adic arithmetic geometry, quadratic forms, algebraic groups, essential dimension theory. The material will be of interest to researchers in these and neighboring fields. Mathematics bicssc Festschriften msc Biographies, obituaries, personalia, bibliographies msc Chernousov edt Garibaldi edt Fesenko edt Friedlander edt Rehmann edt Reichstein edt https://ems.press/doi/10.4171/dms/7 cover image https://content.ems.press/assets/public/images/books/cover-253.png nam a22 5a 4500 10.4171/dms/8 DE-4084 2019-01-01 a fot 00| 0| cr nn mmmmamaa 190101e20190101gw fot 00| 0|eng d 10.4171/dms/8 doi DE-4084 PB bicssc 01A70 msc 11-03 msc Baake edt The Legacy of Kurt Mahler ; A Mathematical Selecta. EMS Press 2019 1 online resource (679 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Documenta Mathematica Series (dms) 8 2943-4998 Free to read https://ems.press/books Kurt Mahler was born at Krefeld am Rhein in Germany in 1903, and died in Canberra, Australia in 1988. Although he lived outside of Germany from 1933 onwards, his mathematical roots were always in the great school of number theory which flourished in Germany between the two World Wars. Thus it is very fitting that Documenta Mathematica should publish this extra volume about the continuing impact of his work today. Mathematics bicssc Biographies, obituaries, personalia, bibliographies msc History of number theory msc Bugeaud edt Coons edt https://ems.press/doi/10.4171/dms/8 cover image https://content.ems.press/assets/public/images/books/cover-252.jpg nam a22 5a 4500 10.4171/etb/25 DE-4084 2023-05-10 a fot 00| 0| cr nn mmmmamaa 230510e20230510gw fot 00| 0|eng d 9783985475506 10.4171/etb/25 doi DE-4084 PB bicssc 49Q22 msc 60B05 msc 28A33 msc 35A15 msc 35Q35 msc 49N15 msc 28A50 msc Figalli aut An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows ; Second Edition. EMS Press 2023 1 online resource (152 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 25 2943-4955 Restricted to subscribers. https://ems.press/books This book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this beautiful subject. The presentation focuses on the essential topics of the theory: Kantorovich duality, existence and uniqueness of optimal transport maps, Wasserstein distances, the JKO scheme, Ottos calculus, and Wasserstein gradient flows. At the end, a presentation of some selected applications of optimal transport is given. Suitable for a course at the graduate level, the book also includes an appendix with a series of exercises along with their solutions. The present second edition contains a number of additions, such as a new section on the Brunn-Minkowski inequality, new exercises, and various corrections throughout the text. For the first edition of this book, please click [here](https://doi.org/10.4171/etb/22). Mathematics bicssc Optimal transportation msc Probability measures on topological spaces msc Spaces of measures, convergence of measures msc Variational methods applied to PDEs msc PDEs in connection with fluid mechanics msc Duality theory (optimization) msc Integration and disintegration of measures msc Glaudo aut https://ems.press/doi/10.4171/etb/25 cover image https://content.ems.press/assets/public/images/books/cover-258.png nam a22 5a 4500 10.4171/mems/5 DE-4084 2023-07-11 a fot 00| 0| cr nn mmmmamaa 230711e20230711gw fot 00| 0|eng d 9783985475568 10.4171/mems/5 doi DE-4084 PB bicssc 46E36 msc 31E05 msc 28A80 msc 31C45 msc 31C25 msc 30L10 msc Kigami aut Conductive Homogeneity of Compact Metric Spaces and Construction of -Energy. EMS Press 2023 1 online resource (138 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 5 2747-9099 Open Access https://ems.press/books In the ordinary theory of Sobolev spaces on domains of , the -energy is defined as the integral of ||. In this paper, we try to construct a -energy on compact metric spaces as a scaling limit of discrete -energies on a series of graphs approximating the original space. In conclusion, we propose a notion called conductive homogeneity under which one can construct a reasonable -energy if p is greater than the Ahlfors regular conformal dimension of the space. In particular, if 2, then we construct a local regular Dirichlet form and show that the heat kernel associated with the Dirichlet form satisfies upper and lower sub-Gaussian type heat kernel estimates. As examples of conductively homogeneous spaces, we present new classes of square-based self-similar sets and rationally ramified Sierpiński crosses, where no diffusions were constructed before. Mathematics bicssc Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces msc Potential theory on fractals and metric spaces msc Fractals msc Other generalizations (nonlinear potential theory, etc.) msc Dirichlet forms msc Quasiconformal mappings in metric spaces msc https://ems.press/doi/10.4171/mems/5 cover image https://content.ems.press/assets/public/images/books/cover-261.jpeg nam a22 5a 4500 10.4171/mems/6 DE-4084 2023-08-11 a fot 00| 0| cr nn mmmmamaa 230811e20230811gw fot 00| 0|eng d 9783985475575 10.4171/mems/6 doi DE-4084 PB bicssc 11F32 msc 11F85 msc 11G07 msc 11G18 msc Buium aut Purely Arithmetic PDEs Over a -Adic Field: -Characters and -Modular Forms. EMS Press 2023 1 online resource (116 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 6 2747-9099 Open Access https://ems.press/books A formalism of arithmetic partial differential equations (PDEs) is being developed in which one considers several arithmetic differentiations at one fixed prime. In this theory solutions can be defined in algebraically closed -adic fields. As an application we show that for at least two arithmetic directions every elliptic curve possesses a non-zero arithmetic PDE Manin map of order 1; such maps do not exist in the arithmetic ODE case. Similarly, we construct and study genuinely PDE differential modular forms. As further applications we derive a Theorem of the kernel and a Reciprocity theorem for arithmetic PDE Manin maps and also a finiteness Diophantine result for modular parameterizations. We also prove structure results for the spaces of PDE differential modular forms defined on the ordinary locus. We also produce a system of differential equations satisfied by our PDE modular forms based on Serre and Euler operators. Mathematics bicssc Modular correspondences, etc. msc \(p\)-adic theory, local fields msc Elliptic curves over local fields msc Arithmetic aspects of modular and Shimura varieties msc Miller aut https://ems.press/doi/10.4171/mems/6 cover image https://content.ems.press/assets/public/images/books/cover-266.png nam a22 5a 4500 10.4171/zlam/30 DE-4084 2023-06-12 a fot 00| 0| cr nn mmmmamaa 230612e20230612gw fot 00| 0|eng d 9783985475537 10.4171/zlam/30 doi DE-4084 PB bicssc 62G20 msc 35R30 msc 65C05 msc Nickl aut Bayesian Non-linear Statistical Inverse Problems. EMS Press 2023 1 online resource (171 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 30 2943-4971 Restricted to subscribers. https://ems.press/books Bayesian methods based on Gaussian process priors are frequently used in statistical inverse problems arising with partial differential equations (PDEs). They can be implemented by Markov chain Monte Carlo (MCMC) algorithms. The underlying statistical models are naturally high- or infinite-dimensional and the present book presents a rigorous mathematical analysis of the statistical performance, and algorithmic complexity, of such methods in a natural setting of non-linear random design regression. Due to the non-linearity present in many of these inverse problems, natural least squares functionals are non-convex and the Bayesian paradigm presents an attractive alternative to optimisation-based approaches. This book develops a general theory of Bayesian inference for non-linear forward maps and rigorously considers two PDE model examples arising with Darcys problem and a Schrödinger equation. The focus is initially on statistical consistency of Gaussian process methods, and then moves on to study local fluctuations and approximations of posterior distributions by Gaussian or log-concave measures whose curvature is described by PDE mapping properties of underlying information operators. Applications to the algorithmic runtime of gradient-based MCMC methods are discussed as well as computation time lower bounds for worst case performance of some algorithms. Mathematics bicssc Asymptotic properties of nonparametric inference msc Inverse problems for PDEs msc Monte Carlo methods msc https://ems.press/doi/10.4171/zlam/30 cover image https://content.ems.press/assets/public/images/books/cover-260.png nam a22 5a 4500 10.4171/zlam/31 DE-4084 2023-09-07 a fot 00| 0| cr nn mmmmamaa 230907e20230907gw fot 00| 0|eng d 9783985475520 10.4171/zlam/31 doi DE-4084 PB bicssc 58J05 msc 35B33 msc 35J60 msc 35J20 msc 58E05 msc 53C21 msc 53-02 msc Malchiodi aut Prescribing Scalar Curvature in Conformal Geometry. EMS Press 2023 1 online resource (161 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 31 2943-4971 Restricted to subscribers. https://ems.press/books This book treats the classical problem, posed by Kazdan and Warner, of prescribing a given function on a closed manifold as the scalar curvature of a metric within a conformal class. Since both critical equations and obstructions to the existence of solutions appear, the problem is particularly challenging. Our focus is to present a general approach for understanding the matter, particularly the issue of loss of compactness. The task of establishing existence of solutions is attacked combining several tools: the variational structure of the problem, Liouville-type theorems, blow-up analysis, elliptic regularity theory, and topological arguments. Treating different aspects of the subject and containing several references to up-to-date research directions and perspectives, the book will be useful to graduate students and researchers interested in geometric analysis and partial differential equations. Mathematics bicssc Elliptic equations on manifolds, general theory msc Critical exponents in context of PDEs msc Nonlinear elliptic equations msc Variational methods for second-order elliptic equations msc Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces msc Methods of global Riemannian geometry, including PDE methods; curvature restrictions msc Research exposition (monographs, survey articles) pertaining to differential geometry msc https://ems.press/doi/10.4171/zlam/31 cover image https://content.ems.press/assets/public/images/books/cover-268.png nam a22 5a 4500 10.4171/etm/36 DE-4084 2023-11-27 a fot 00| 0| cr nn mmmmamaa 231127e20231127gw fot 00| 0|eng d 9783985475483 10.4171/etm/36 doi DE-4084 PB bicssc 22-02 msc 22A05 msc 22D05 msc 22E20 msc 22E65 msc Hofmann aut The Structure of Pro-Lie Groups. EMS Press 2023 1 online resource (840 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 36 2943-5005 Restricted to subscribers. https://ems.press/books <p>Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonné quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them.</p> <p>A *pro-Lie group* is a complete topological group *G* in which every identity neighborhood *U* of *G* contains a normal subgroup *N* such that the quotient *G/N* is a Lie group. Every locally compact connected topological group and every compact group is a pro-Lie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of pro-Lie groups is.</p> <p>For half a century, locally compact pro-Lie groups have drifted through the literature, yet this is the first book which systematically treats the Lie theory and the structure theory of pro-Lie groups irrespective of local compactness. So it fits very well into that current trend which addresses infinite dimensional Lie groups. The results of this text are based on a theory of pro-Lie algebras which parallels the structure theory of finite dimensional real Lie algebras to an astonishing degree even though it has to overcome technical obstacles.</p> <p>A topological group is said to be almost connected if the quotient group of its connected components is compact. This book exposes a Lie theory of almost connected pro-Lie groups (and hence of almost connected locally compact groups) and illuminates the variety of ways in which their structure theory reduces to that of compact groups on the one hand and of finite dimensional Lie groups on the other. It is therefore a continuation of the authors' monograph on the structure of compact groups (1998, 2006, 2014, 2020, 2023) and is an invaluable tool for researchers in topological groups, Lie theory, harmonic analysis and representation theory. It is written to be accessible to advanced graduate students wishing to study this fascinating and important area of research, which has so many fruitful interactions with other fields of mathematics.</p> <p>For the first edition of this book, please click [here](https://ems.press/books/etm/37).</p> Mathematics bicssc Research exposition (monographs, survey articles) pertaining to topological groups msc Structure of general topological groups msc General properties and structure of locally compact groups msc General properties and structure of other Lie groups msc Infinite-dimensional Lie groups and their Lie algebras: general properties msc Morris aut https://ems.press/doi/10.4171/etm/36 cover image https://content.ems.press/assets/public/images/books/cover-270.png nam a22 5a 4500 10.4171/irma/34 DE-4084 2023-08-08 a fot 00| 0| cr nn mmmmamaa 230808e20230808gw fot 00| 0|eng d 9783985475247 10.4171/irma/34 doi DE-4084 PB bicssc 00B15 msc 01-02 msc 01-06 msc 01A70 msc 14B05 msc 34M35 msc 57K20 msc 57R45 msc 32S05 msc 32S55 msc 57K12 msc 57R17 msc 57K45 msc 57K30 msc 57K45 msc 00A30 msc 57K10 msc 57K16 msc 58K30 msc 51M15 msc 53C70 msc Papadopoulos edt Essays in Geometry ; Dedicated to Norbert ACampo. EMS Press 2023 1 online resource (1028 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 34 2523-5141 Restricted to subscribers. https://ems.press/books This volume consists in a collection of essays dedicated to Norbert A'Campo on the occasion of his 80th birthday. The subject is geometry in the broadest sense. The topics include hyperbolic and super hyperbolic geometry, 3-manifolds, metric geometry, mapping class groups, linear groups, Riemann surfaces, Teichmüller spaces, high-dimensional complex geometry, differential topology, symplectic geometry, singularity theory, number theory, algebraic geometry, dynamics, mathematical physics and philosophy of mathematics. The book gives a fairly comprehensive overview of the wealth of current research in geometry. Mathematics bicssc Collections of articles of miscellaneous specific interest msc Research exposition (monographs, survey articles) pertaining to history and biography msc Proceedings, conferences, collections, etc. pertaining to history and biography msc Biographies, obituaries, personalia, bibliographies msc Singularities in algebraic geometry msc Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms msc 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) msc Singularities of differentiable mappings in differential topology msc Local complex singularities msc Milnor fibration; relations with knot theory msc Generalized knots (virtual knots, welded knots, quandles, etc.) msc Symplectic and contact topology in high or arbitrary dimension msc Higher-dimensional knots and links msc General topology of 3-manifolds msc Higher-dimensional knots and links msc Philosophy of mathematics msc Knot theory msc Finite-type and quantum invariants, topological quantum field theories (TQFT) msc Global theory of singularities msc Geometric constructions in real or complex geometry msc Direct methods (\(G\)-spaces of Busemann, etc.) msc https://ems.press/doi/10.4171/irma/34 cover image https://content.ems.press/assets/public/images/books/cover-265.png nam a22 5a 4500 10.4171/mems/7 DE-4084 2023-10-07 a fot 00| 0| cr nn mmmmamaa 231007e20231007gw fot 00| 0|eng d 9783985475551 10.4171/mems/7 doi DE-4084 PB bicssc 76T20 msc 35R60 msc 76M50 msc 35Q35 msc 76D03 msc 76D07 msc 60G55 msc Duerinckx aut On Einstein's Effective Viscosity Formula. EMS Press 2023 1 online resource (196 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 7 2747-9099 Open Access https://ems.press/books <p>In his PhD thesis, Einstein derived an explicit first-order expansion for the effective viscosity of a Stokes fluid with a suspension of small rigid particles at low density. His formal derivation relied on two implicit assumptions: (i) there is a scale separation between the size of the particles and the observation scale; and (ii) at first order, dilute particles do not interact with one another. In mathematical terms, the first assumption amounts to the validity of a homogenization result defining the effective viscosity tensor, which is now well understood. Next, the second assumption allowed Einstein to approximate this effective viscosity at low density by considering particles as being isolated. The rigorous justification is, in fact, quite subtle as the effective viscosity is a nonlinear nonlocal function of the ensemble of particles and as hydrodynamic interactions have borderline integrability. </p> <p>In the present memoir, we establish Einstein's effective viscosity formula in the most general setting. In addition, we pursue the low-density expansion to arbitrary order in form of a cluster expansion, where the summation of hydrodynamic interactions crucially requires suitable renormalizations. In particular, we justify a celebrated result by Batchelor and Green on the second-order correction and we explicitly describe all higher-order renormalizations for the first time. In some specific settings, we further address the summability of the whole cluster expansion. Our approach relies on a combination of combinatorial arguments, variational analysis, elliptic regularity, probability theory, and diagrammatic integration methods.</p> Mathematics bicssc Suspensions msc PDEs with randomness, stochastic partial differential equations msc Homogenization applied to problems in fluid mechanics msc PDEs in connection with fluid mechanics msc Existence, uniqueness, and regularity theory for incompressible viscous fluids msc Stokes and related (Oseen, etc.) flows msc Point processes (e.g., Poisson, Cox, Hawkes processes) msc Gloria aut https://ems.press/doi/10.4171/mems/7 cover image https://content.ems.press/assets/public/images/books/cover-269.png nam a22 5a 4500 10.4171/ecr/19 DE-4084 2023-11-30 a fot 10| 0| cr nn mmmmamaa 231130e20231130gw fot 10| 0|eng d 9783985475544 10.4171/ecr/19 doi DE-4084 PB bicssc 16-06 msc 18-06 msc 13-06 msc 14-06 msc Buan edt Representations of Algebras and Related Structures ; International Conference on Representations of Algebras, ICRA 2020, 9-25 November 2020. EMS Press 2023 1 online resource (428 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 19 2523-5168 Restricted to subscribers. https://ems.press/books This volume presents a collection of articles devoted to representations of algebras and related topics. Distinguished experts in this field presented their work at the International Conference on Representations of Algebras in 2020. The book reflects recent trends in the representation theory of algebras and its interactions with other central branches of mathematics, including combinatorics, commutative algebra, algebraic geometry, topology, data analysis, Lie algebras, quantum groups, homological algebra, and theoretical physics. There are thirteen independent articles, written by leading experts in the field. Most are expository survey papers, but some are also original research contributions. This collection is addressed to researchers and graduate students in algebra as well as to a broader mathematical audience. It contains open problems and new perspectives for research in the field. Mathematics bicssc Proceedings, conferences, collections, etc. pertaining to associative rings and algebras msc Proceedings, conferences, collections, etc. pertaining to category theory msc Proceedings, conferences, collections, etc. pertaining to commutative algebra msc Proceedings, conferences, collections, etc. pertaining to algebraic geometry msc Krause edt Solberg edt https://ems.press/doi/10.4171/ecr/19 cover image https://content.ems.press/assets/public/images/books/cover-271.png nam a22 5a 4500 10.4171/icm2022 DE-4084 2023-12-15 a fot 10| 0| cr nn mmmmamaa 231215e20231215gw fot 10| 0|eng d 9783985475582 10.4171/icm2022 doi DE-4084 PB bicssc 00B25 msc Beliaev edt International Congress of Mathematicians ; 2022 July 6-14. EMS Press 2023 1 online resource (5940 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Open Access https://ems.press/books Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022. Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress. The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library. The contents of the ICM 2022 Proceedings are available online with open access. Mathematics bicssc Proceedings of conferences of miscellaneous specific interest msc Smirnov edt https://ems.press/doi/10.4171/icm2022 cover image https://content.ems.press/assets/public/images/books/cover-272.png nam a22 5a 4500 10.4171/icm2022-1 DE-4084 2023-12-15 a fot 10| 0| cr nn mmmmamaa 231215e20231215gw fot 10| 0|eng d 9783985475599 10.4171/icm2022-1 doi DE-4084 PB bicssc 00B25 msc Beliaev edt International Congress of Mathematicians ; 2022 July 6-14. Volume I. Prize Lectures EMS Press 2023 1 online resource (596 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Open Access https://ems.press/books Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022. Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress. The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library. The contents of the ICM 2022 Proceedings are available online with open access. Mathematics bicssc Proceedings of conferences of miscellaneous specific interest msc Smirnov edt https://ems.press/doi/10.4171/icm2022-1 cover image https://content.ems.press/assets/public/images/books/cover-273.png nam a22 5a 4500 10.4171/icm2022-2 DE-4084 2023-12-15 a fot 10| 0| cr nn mmmmamaa 231215e20231215gw fot 10| 0|eng d 9783985475605 10.4171/icm2022-2 doi DE-4084 PB bicssc 00B25 msc Beliaev edt International Congress of Mathematicians ; 2022 July 6-14. Volume II. Plenary Lectures EMS Press 2023 1 online resource (880 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Open Access https://ems.press/books Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022. Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress. The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library. The contents of the ICM 2022 Proceedings are available online with open access. Mathematics bicssc Proceedings of conferences of miscellaneous specific interest msc Smirnov edt https://ems.press/doi/10.4171/icm2022-2 cover image https://content.ems.press/assets/public/images/books/cover-274.png nam a22 5a 4500 10.4171/icm2022-3 DE-4084 2023-12-15 a fot 10| 0| cr nn mmmmamaa 231215e20231215gw fot 10| 0|eng d 9783985475612 10.4171/icm2022-3 doi DE-4084 PB bicssc 00B25 msc Beliaev edt International Congress of Mathematicians ; 2022 July 6-14. Volume III. Sections 1-4 EMS Press 2023 1 online resource (952 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Open Access https://ems.press/books Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022. Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress. The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library. The contents of the ICM 2022 Proceedings are available online with open access. Mathematics bicssc Proceedings of conferences of miscellaneous specific interest msc Smirnov edt https://ems.press/doi/10.4171/icm2022-3 cover image https://content.ems.press/assets/public/images/books/cover-275.png nam a22 5a 4500 10.4171/icm2022-4 DE-4084 2023-12-15 a fot 10| 0| cr nn mmmmamaa 231215e20231215gw fot 10| 0|eng d 9783985475629 10.4171/icm2022-4 doi DE-4084 PB bicssc 00B25 msc Beliaev edt International Congress of Mathematicians ; 2022 July 6-14. Volume IV. Sections 5-8 EMS Press 2023 1 online resource (1016 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Open Access https://ems.press/books Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022. Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress. The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library. The contents of the ICM 2022 Proceedings are available online with open access. Mathematics bicssc Proceedings of conferences of miscellaneous specific interest msc Smirnov edt https://ems.press/doi/10.4171/icm2022-4 cover image https://content.ems.press/assets/public/images/books/cover-276.png nam a22 5a 4500 10.4171/icm2022-5 DE-4084 2023-12-15 a fot 10| 0| cr nn mmmmamaa 231215e20231215gw fot 10| 0|eng d 9783985475636 10.4171/icm2022-5 doi DE-4084 PB bicssc 00B25 msc Beliaev edt International Congress of Mathematicians ; 2022 July 6-14. Volume V. Sections 9-11 EMS Press 2023 1 online resource (812 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Open Access https://ems.press/books Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022. Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress. The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library. The contents of the ICM 2022 Proceedings are available online with open access. Mathematics bicssc Proceedings of conferences of miscellaneous specific interest msc Smirnov edt https://ems.press/doi/10.4171/icm2022-5 cover image https://content.ems.press/assets/public/images/books/cover-277.png nam a22 5a 4500 10.4171/icm2022-6 DE-4084 2023-12-15 a fot 10| 0| cr nn mmmmamaa 231215e20231215gw fot 10| 0|eng d 9783985475643 10.4171/icm2022-6 doi DE-4084 PB bicssc 00B25 msc Beliaev edt International Congress of Mathematicians ; 2022 July 6-14. Volume VI. Sections 12-14 EMS Press 2023 1 online resource (880 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Open Access https://ems.press/books Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022. Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress. The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library. The contents of the ICM 2022 Proceedings are available online with open access. Mathematics bicssc Proceedings of conferences of miscellaneous specific interest msc Smirnov edt https://ems.press/doi/10.4171/icm2022-6 cover image https://content.ems.press/assets/public/images/books/cover-278.png nam a22 5a 4500 10.4171/icm2022-7 DE-4084 2023-12-15 a fot 10| 0| cr nn mmmmamaa 231215e20231215gw fot 10| 0|eng d 9783985475650 10.4171/icm2022-7 doi DE-4084 PB bicssc 00B25 msc Beliaev edt International Congress of Mathematicians ; 2022 July 6-14. Volume VII. Sections 15-20 EMS Press 2023 1 online resource (804 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Open Access https://ems.press/books Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022. Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress. The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library. The contents of the ICM 2022 Proceedings are available online with open access. Mathematics bicssc Proceedings of conferences of miscellaneous specific interest msc Smirnov edt https://ems.press/doi/10.4171/icm2022-7 cover image https://content.ems.press/assets/public/images/books/cover-279.png nam a22 5a 4500 10.4171/mems/8 DE-4084 2024-02-02 a fot 00| 0| cr nn mmmmamaa 240202e20240202gw fot 00| 0|eng d 9783985475667 10.4171/mems/8 doi DE-4084 PB bicssc 19K35 msc 19K33 msc 46L05 msc 46L80 msc 46L85 msc Willett aut The Universal Coefficient Theorem for *-Algebras with Finite Complexity. EMS Press 2024 1 online resource (108 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 8 2747-9099 Open Access https://ems.press/books A *-algebra satisfies the Universal Coefficient Theorem (UCT) of Rosenberg and Schochet if it is equivalent in Kasparov's KK-theory to a commutative *-algebra. This paper is motivated by the problem of establishing the range of validity of the UCT, and in particular, whether the UCT holds for all nuclear *-algebras. We introduce the idea of a *-algebra that decomposes over a class of *-algebras. Roughly, this means that locally there are approximately central elements that approximately cut the *-algebra into two *-subalgebras from that have well-behaved intersection. We show that if a *-algebra decomposes over the class of nuclear, UCT *-algebras, then it satisfies the UCT. The argument is based on a Mayer-Vietoris principle in the framework of controlled KK-theory; the latter was introduced by the authors in an earlier work. Nuclearity is used via Kasparov's Hilbert module version of Voiculescu's theorem, and Haagerup's theorem that nuclear *-algebras are amenable. We say that a *-algebra has finite complexity if it is in the smallest class of *-algebras containing the finite-dimensional *-algebras, and closed under decomposability; our main result implies that all *-algebras in this class satisfy the UCT. The class of *-algebras with finite complexity is large, and comes with an ordinal-number invariant measuring the complexity level. We conjecture that a *-algebra of finite nuclear dimension and real rank zero has finite complexity; this (and several other related conjectures) would imply the UCT for all separable nuclear *-algebras. We also give new local formulations of the UCT, and some other necessary and sufficient conditions for the UCT to hold for all nuclear *-algebras. Mathematics bicssc Kasparov theory (\(KK\)-theory) msc Ext and \(K\)-homology msc General theory of \(C^*\)-algebras msc \(K\)-theory and operator algebras (including cyclic theory) msc Noncommutative topology msc Yu aut https://ems.press/doi/10.4171/mems/8 cover image https://content.ems.press/assets/public/images/books/cover-280.png nam a22 5a 4500 10.4171/mems/9 DE-4084 2024-02-02 a fot 00| 0| cr nn mmmmamaa 240202e20240202gw fot 00| 0|eng d 9783985475674 10.4171/mems/9 doi DE-4084 PB bicssc 22E66 msc 17B15 msc 17B56 msc 17B65 msc 17B66 msc 17B67 msc 17B81 msc 22E60 msc 22E65 msc 22E67 msc Janssens aut Positive Energy Representations of Gauge Groups I ; Localization. EMS Press 2024 1 online resource (156 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 9 2747-9099 Open Access https://ems.press/books This is the first in a series of papers on projective positive energy representations of gauge groups. Let be a principal fiber bundle, and let _c(,Ad ()) be the group of compactly supported (local) gauge transformations. If is a group of "space-time symmetries" acting on , then a projective unitary representation of _c(,Ad()) is of *positive energy* if every "timelike generator" ₀ gives rise to a Hamiltonian (₀) whose spectrum is bounded from below. Our main result shows that in the absence of fixed points for the cone of timelike generators, the projective positive energy representations of the connected component _c(,Ad())₀ come from 1-dimensional -orbits. For compact this yields a complete classification of the projective positive energy representations in terms of lowest weight representations of affine Kac-Moody algebras. For noncompact , it yields a classification under further restrictions on the space of ground states. In the second part of this series we consider larger groups of gauge transformations, which contain also global transformations. The present results are used to localize the positive energy representations at (conformal) infinity. Mathematics bicssc Analysis on and representations of infinite-dimensional Lie groups msc Representations of Lie algebras and Lie superalgebras, analytic theory msc Cohomology of Lie (super)algebras msc Infinite-dimensional Lie (super)algebras msc Lie algebras of vector fields and related (super) algebras msc Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras msc Applications of Lie (super)algebras to physics, etc. msc Lie algebras of Lie groups msc Infinite-dimensional Lie groups and their Lie algebras: general properties msc Loop groups and related constructions, group-theoretic treatment msc Neeb aut https://ems.press/doi/10.4171/mems/9 cover image https://content.ems.press/assets/public/images/books/cover-281.png nam a22 5a 4500 10.4171/mems/10 DE-4084 2024-02-02 a fot 00| 0| cr nn mmmmamaa 240202e20240202gw fot 00| 0|eng d 9783985475681 10.4171/mems/10 doi DE-4084 PB bicssc 92-10 msc 35Q92 msc 60G07 msc 35Q93 msc 60G22 msc 35R11 msc Dipierro aut The Lévy Flight Foraging Hypothesis in Bounded Regions ; Subordinate Brownian Motions and High-risk/High-gain Strategies. EMS Press 2024 1 online resource (99 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 10 2747-9099 Open Access https://ems.press/books We investigate the problem of the Lévy flight foraging hypothesis in an ecological niche described by a bounded region of space, with either absorbing or reflecting boundary conditions. To this end, we consider a forager diffusing according to a fractional heat equation in a bounded domain and we define several efficiency functionals whose optimality is discussed in relation to the fractional exponent (0, 1) of the diffusive equation. Such an equation is taken to be the spectral fractional heat equation (with Dirichlet or Neumann boundary conditions). We analyze the biological scenarios in which a target is close to the forager or far from it. In particular, for all the efficiency functionals considered here, we show that if the target is close enough to the forager, then the most rewarding search strategy will be in a small neighborhood of 0. Interestingly, we show that 0 is a global pessimizer for some of the efficiency functionals. From this, together with the aforementioned optimality results, we deduce that the most rewarding strategy can be unsafe or unreliable in practice, given its proximity with the pessimizing exponent, thus the forager may opt for a less performant, but safer, hunting method. The biological literature has collected several pieces of evidence of foragers diffusing with very low Lévy exponents, often in relation with a high energetic content of the prey. It is thereby suggestive to relate these patterns, which are induced by distributions with a very fat tail, with a high-risk/high-gain strategy, in which the forager adopts a potentially very profitable, but also potentially completely unrewarding, strategy due to the high value of the possible outcome. Mathematics bicssc Mathematical modeling or simulation for problems pertaining to biology msc PDEs in connection with biology, chemistry and other natural sciences msc General theory of stochastic processes msc PDEs in connection with control and optimization msc Fractional processes, including fractional Brownian motion msc Fractional partial differential equations msc Giacomin aut Valdinoci aut https://ems.press/doi/10.4171/mems/10 cover image https://content.ems.press/assets/public/images/books/cover-282.png nam a22 5a 4500 10.4171/mems/12 DE-4084 2024-04-01 a fot 00| 0| cr nn mmmmamaa 240401e20240401gw fot 00| 0|eng d 9783985475711 10.4171/mems/12 doi DE-4084 PB bicssc 81S30 msc 35P05 msc 42B20 msc 47G10 msc 47G30 msc 47N70 msc 94A12 msc Lerner aut Integrating the Wigner Distribution on Subsets of the Phase Space, a Survey. EMS Press 2024 1 online resource (224 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 12 2747-9099 Open Access https://ems.press/books We review several properties of integrals of the Wigner distribution on subsets of the phase space. Along our way, we provide a theoretical proof of the invalidity of Flandrins conjecture, a fact already proven via numerical arguments in our joint paper \[J. Fourier Anal. Appl. 26 (2020), no. 1, article no. 6\] with B. Delourme and T. Duyckaerts. We use also the J.G. Wood & A.J. Bracken paper \[J. Math. Phys. 46 (2005), no. 4, article no. 042103\], for which we offer a mathematical perspective. We review thoroughly the case of subsets of the plane whose boundary is a conic curve and show that Mehlers formula can be helpful in the analysis of these cases, including for the higher dimensional case investigated in the paper \[J. Math. Phys. 51 (2010), no. 10, article no. 102101\] by E. Lieb and Y. Ostrover. Using the Feichtinger algebra, we show that, generically in the Baire sense, the Wigner distribution of a pulse in ²() does not belong to ¹(²), providing as a byproduct a large class of examples of subsets of the phase space ² on which the integral of the Wigner distribution is infinite. We study as well the case of convex polygons of the plane, with a rather weak estimate depending on the number of vertices, but independent of the area of the polygon. Mathematics bicssc Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics msc General topics in linear spectral theory for PDEs msc Singular and oscillatory integrals (Calderón-Zygmund, etc.) msc Integral operators msc Pseudodifferential operators msc Applications of operator theory in systems, signals, circuits, and control theory msc Signal theory (characterization, reconstruction, filtering, etc.) msc https://ems.press/doi/10.4171/mems/12 cover image https://content.ems.press/assets/public/images/books/cover-284.png nam a22 5a 4500 10.4171/mems/11 DE-4084 2024-03-31 a fot 00| 0| cr nn mmmmamaa 240331e20240331gw fot 00| 0|eng d 9783985475698 10.4171/mems/11 doi DE-4084 PB bicssc 51F30 msc 46B07 msc 52A23 msc 46B06 msc 46B20 msc 46B85 msc 54C20 msc Naor aut Extension, Separation and Isomorphic Reverse Isoperimetry. EMS Press 2024 1 online resource (242 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 11 2747-9099 Open Access https://ems.press/books The Lipschitz extension modulus e() of a metric space is the infimum over those \[1,\] such that for any Banach space and any , any 1-Lipschitz function : can be extended to an -Lipschitz function :. Johnson, Lindenstrauss and Schechtman proved (1986) that if is an -dimensional normed space, then e(). In the reverse direction, we prove that every -dimensional normed space satisfies e(), where >0 is a universal constant. Our core technical contribution is a geometric structural result on stochastic clustering of finite dimensional normed spaces which implies upper bounds on their Lipschitz extension moduli using an extension method of Lee and the author (2005). The separation modulus of a metric space (,) is the infimum over those (0,\] such that for any >0 there is a distribution over random partitions of into clusters of diameter at most such that for every two points , the probability that they belong to different clusters is at most (,)/. We obtain upper and lower bounds on the separation moduli of finite dimensional normed spaces that relate them to well-studied volumetric invariants (volume ratios and projection bodies). Using these connections, we determine the asymptotic growth rate of the separation moduli of various normed spaces. If is an -dimensional normed space with enough symmetries, then our bounds imply that its separation modulus is equal to vr (^*) up to factors of lower order, where vr(^\*) (^\*) is the volume ratio of the unit ball of the dual of . We formulate a conjecture on isomorphic reverse isoperimetric properties of symmetric convex bodies (akin to Balls reverse isoperimetric theorem (1991), but permitting a non-isometric perturbation in addition to the choice of position) that can be used with our volumetric bounds on the separation modulus to obtain many more exact asymptotic evaluations of the separation moduli of normed spaces. Our estimates on the separation modulus imply asymptotically improved upper bounds on the Lipschitz extension moduli of various classical spaces. In particular, we deduce an improved upper bound on e() when >2 that resolves a conjecture of Brudnyi and Brudnyi (2005), and we prove that e(), which is the first time that the growth rate of e() has been evaluated (as dim()) for *any* finite dimensional normed space . Mathematics bicssc Lipschitz and coarse geometry of metric spaces msc Local theory of Banach spaces msc Asymptotic theory of convex bodies msc Asymptotic theory of Banach spaces msc Geometry and structure of normed linear spaces msc Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science msc Extension of maps msc https://ems.press/doi/10.4171/mems/11 cover image https://content.ems.press/assets/public/images/books/cover-283.png nam a22 5a 4500 10.4171/mems/13 DE-4084 2024-05-07 a fot 00| 0| cr nn mmmmamaa 240507e20240507gw fot 00| 0|eng d 9783985475704 10.4171/mems/13 doi DE-4084 PB bicssc 65D15 msc 41A10 msc Adcock aut On Efficient Algorithms for Computing Near-Best Polynomial Approximations to High-Dimensional, Hilbert-Valued Functions from Limited Samples. EMS Press 2024 1 online resource (112 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 13 2747-9099 Open Access https://ems.press/books Sparse polynomial approximation is an important tool for approximating high-dimensional functions from limited samples - a task commonly arising in computational science and engineering. Yet, it lacks a complete theory. There is a well-developed theory of *best s-term polynomial approximation*, which asserts exponential or algebraic rates of convergence for holomorphic functions. There are also increasingly mature methods such as (weighted) ²-minimization for practically computing such approximations. However, whether these methods achieve the rates of the best s-term approximation is not fully understood. Moreover, these methods are not algorithms per se, since they involve exact minimizers of nonlinear optimization problems. This paper closes these gaps by affirmatively answering the following question: *are there robust, efficient algorithms for computing sparse polynomial approximations to finite- or infinite-dimensional, holomorphic and Hilbert-valued functions from limited samples that achieve the same rates as the best s-term approximation?* We do so by introducing algorithms with exponential or algebraic convergence rates that are also robust to *sampling*, *algorithmic* and *physical discretization* errors. Our results involve several developments of existing techniques, including a new restarted primal-dual iteration for solving weighted \ell^1-minimization problems in Hilbert spaces. Our theory is supplemented by numerical experiments demonstrating the efficacy of these algorithms. Mathematics bicssc Algorithms for approximation of functions msc Approximation by polynomials msc Brugiapaglia aut Dexter aut Moraga aut https://ems.press/doi/10.4171/mems/13 cover image https://content.ems.press/assets/public/images/books/cover-285.png nam a22 5a 4500 10.4171/zlam/32 DE-4084 2024-05-07 a fot 00| 0| cr nn mmmmamaa 240507e20240507gw fot 00| 0|eng d 9783985475742 10.4171/zlam/32 doi DE-4084 PB bicssc 82D30 msc 35F21 msc 62B10 msc 60K35 msc Dominguez aut Statistical Mechanics of Mean-Field Disordered Systems ; A Hamilton-Jacobi Approach. EMS Press 2024 1 online resource (367 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Zurich Lectures in Advanced Mathematics (zlam) 32 2943-4971 Restricted to subscribers. https://ems.press/books The goal of this book is to present new mathematical techniques for studying the behavior of mean-field systems with disordered interactions. We mostly focus on certain problems of statistical inference in high dimension, and on spin glasses. The techniques we present aim to determine the free energy of these systems, in the limit of large system size, by showing that they asymptotically satisfy a Hamilton-Jacobi equation. The first chapter is a general introduction to statistical mechanics, with a focus on the Curie-Weiss model. We give a brief introduction to convex analysis and large deviation principles in Chapter 2, and identify the limit free energy of the Curie-Weiss model using these tools. In Chapter 3, we define the notion of viscosity solution to a Hamilton-Jacobi equation, and use it to recover the limit free energy of the Curie-Weiss model. We discover technical challenges to applying the same method to generalized versions of the Curie-Weiss model, and develop a new selection principle based on convexity to overcome these. We then turn to statistical inference in Chapter 4, focusing on the problem of recovering a large symmetric rank-one matrix from a noisy observation, and we see that the tools developed in the previous chapter apply to this setting as well. Chapter 5 is preparatory work for a discussion of the more challenging case of spin glasses. The first half of this chapter is a self-contained introduction to Poisson point processes, including limit theorems on extreme values of independent and identically distributed random variables. We finally turn to the setting of spin glasses in Chapter 6. For the Sherrington-Kirkpatrick model, we show how to relate the Parisi formula with the Hamilton-Jacobi approach. We conclude with a more informal discussion on the status of current research for more challenging models. Mathematics bicssc Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) msc Hamilton-Jacobi equations msc Statistical aspects of information-theoretic topics msc Interacting random processes; statistical mechanics type models; percolation theory msc Mourrat aut https://ems.press/doi/10.4171/zlam/32 cover image https://content.ems.press/assets/public/images/books/cover-286.png nam a22 5a 4500 10.4171/zbl90 DE-4084 2024-06-17 a fot 00| 0| cr nn mmmmamaa 240617e20240617gw fot 00| 0|eng d 9783985475735 10.4171/zbl90 doi DE-4084 01A74 msc 01-06 msc 01A60 msc 01A61 msc 01A65 msc Hulek edt 90 Years of zbMATH. EMS Press 2024 1 online resource (110 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Open Access https://ems.press/books zbMATH Open, the world's most comprehensive and longest-running abstracting and reviewing service in pure and applied mathematics was founded by Otto Neugebauer in 1931. It celebrated its 90th anniversary by becoming an open access database. In December 2019, the Joint Science Conference (Gemeinsame Wissenschaftskonferenz) agreed that the Federal and State Governments of Germany would support FIZ Karlsruhe in transforming zbMATH into an open platform. In future, zbMATH Open will link mathematical services and platforms so as to provide considerably more content for further research and collaborative work in mathematics and related fields. This book presents how zbMATH Open has reacted to a rapidly changing digital era. Topics covered include: the linkage of zbMATH Open with different community platforms and digital maths libraries, the use of zbMATH Open as a bibliographical tool, API solutions, current advancements in author profiles, the indexing of mathematical software packages (swMATH), and issues concerning mathematical formula search in zbMATH Open. We also reflect on the gender publication gap in mathematics, and focus on one of the central pillars of zbMATH Open: the community of reviewers. History of mathematics at institutions and academies (non-university) msc Proceedings, conferences, collections, etc. pertaining to history and biography msc History of mathematics in the 20th century msc History of mathematics in the 21st century msc Development of contemporary mathematics msc Paniagua Taboada edt Teschke edt https://ems.press/doi/10.4171/zbl90 cover image https://content.ems.press/assets/public/images/books/cover-287.png nam a22 5a 4500 10.4171/elm/35 DE-4084 2024-06-26 a fot 00| 0| cr nn mmmmamaa 240626e20240626gw fot 00| 0|eng d 9783985475759 10.4171/elm/35 doi DE-4084 60B20 msc 15B52 msc 46L54 msc 60B10 msc Speicher aut Lectures on Random Matrices. EMS Press 2024 1 online resource (131 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 35 2523-5184 Restricted to subscribers. https://ems.press/books Random matrices are cool In this book we give an idea why random matrices are so fascinating and have become a centrepiece of modern mathematics. This an introduction to random matrix theory, giving an impression of some of the most important aspects of this modern subject. In particular, it covers the basic combinatorial and analytic theory around Wigners semicircle law, featuring also concentration phenomena, and the Tracy-Widom distribution of the largest eigenvalue. The circular law and a discussion of Voiculescus multivariate extension of the semicircle law, as an appetiser for free probability theory, also make an appearance. This book is based on a lecture series for graduate and advanced undergraduate students at Saarland University, Germany. Random matrices (probabilistic aspects) msc Random matrices (algebraic aspects) msc Free probability and free operator algebras msc Convergence of probability measures msc https://ems.press/doi/10.4171/elm/35 cover image https://content.ems.press/assets/public/images/books/cover-288.png nam a22 5a 4500 10.4171/elm/36 DE-4084 2024-08-07 a fot 00| 0| cr nn mmmmamaa 240807e20240807gw fot 00| 0|eng d 9783985475773 10.4171/elm/36 doi DE-4084 PB bicssc 11-01 msc 11D04 msc 11D09 msc 11D45 msc 11D59 msc 11G50 msc Zannier aut Lecture Notes on Diophantine Analysis ; With an Appendix by Francesco Amoroso. EMS Press 2024 1 online resource (411 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 36 2523-5184 Restricted to subscribers. https://ems.press/books The present book is a new, substantially enlarged, version of a previous set of lecture notes on diophantine analysis, published first in 2008, and then in revised form a few years later, by the *Edizioni della Scuola Normale*. The content mixes a number of rather classical results on diophantine equations and diophantine approximation, with the basic theory of heights and a few more recent results and applications of it. The exposition has been generally kept at an elementary and essentially self-contained level, focusing on some main ideas rather than finer technical results which can be obtained by similar methods. In fact, the book is addressed also to readers outside the relevant fields, with the hope that also more expert readers might find something relevant to them. The present second edition contains substantial new material, in the form of new sections, supplements, remarks, and exercises. The arguments for the exercises are developed in full by means of hints, which in fact are much more than scattered suggestions, and practically contain complete details. Occasionally the remarks and the exercises contain miscellaneous results which have not been explicitly published elsewhere. Mathematics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory msc Linear Diophantine equations msc Quadratic and bilinear Diophantine equations msc Counting solutions of Diophantine equations msc Thue-Mahler equations msc Heights msc https://ems.press/doi/10.4171/elm/36 cover image https://content.ems.press/assets/public/images/books/cover-289.png nam a22 5a 4500 10.4171/mems/14 DE-4084 2024-08-21 a fot 00| 0| cr nn mmmmamaa 240821e20240821gw fot 00| 0|eng d 9783985475728 10.4171/mems/14 doi DE-4084 PB bicssc 30-02 msc 30C20 msc 30E10 msc 30H99 msc 54F15 msc Carmona aut Carathéodory Sets in the Plane. EMS Press 2024 1 online resource (146 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 14 2747-9099 Open Access https://ems.press/books This work is devoted to the class of sets in the complex plane which nowadays are known as Carathéodory sets, more precisely speaking, as Carathéodory domains and Carathéodory compact sets. These sets naturally arose many times in various research areas in Real, Complex and Functional Analysis and in the Theory of Partial Differential Equations. For instance, the concept of a Carathéodory set plays a significant role in such topical themes as approximation in the complex plane, the theory of conformal mappings, boundary value problems for elliptic partial differential equations, etc. The first appearance of Carathéodory domains in the mathematical literature (of course, without the special name at that moment) was at the beginning of the 20th century, when C. Carathéodory published his famous series of papers about boundary behavior of conformal mappings. The next breakthrough result which was obtained with the essential help of this concept is the Walsh-Lebesgue criterion for uniform approximation of functions by harmonic polynomials on plane compacta (1929). Up to now the studies of Carathéodory domains and Carathéodory compact sets remains a topical field of contemporary analysis and a number of important results were recently obtained in this direction. Among them one ought to mention the results about polyanalytic polynomial approximation, where the class of Carathéodory compact sets was one of the crucial tools, and the results about boundary behavior of conformal mappings from the unit disk onto Carathéodory domains. Our aim in the present paper is to give a survey on known results related with Carathéodory sets and to present several new results concerning the matter. Starting with the classical works of Carathéodory, Farrell, Walsh, and passing through the history of Complex Analysis of the 20th century, we come to recently obtained results, and to our contribution to the theory. Mathematics bicssc Research exposition (monographs, survey articles) pertaining to functions of a complex variable msc Conformal mappings of special domains msc Approximation in the complex plane msc Spaces and algebras of analytic functions of one complex variable msc Continua and generalizations msc Fedorovskiy aut https://ems.press/doi/10.4171/mems/14 cover image https://content.ems.press/assets/public/images/books/cover-291.png nam a22 5a 4500 10.4171/etb/27 DE-4084 2024-08-19 a fot 00| 0| cr nn mmmmamaa 240819e20240819gw fot 00| 0|eng d 9783985475780 10.4171/etb/27 doi DE-4084 PB bicssc 20-01 msc 20E18 msc 06E15 msc 11F85 msc 18A30 msc 20E06 msc 20E08 msc 20E26 msc 20F65 msc 20J06 msc 57M10 msc Wilkes aut Profinite Groups and Residual Finiteness. EMS Press 2024 1 online resource (434 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Textbooks in Mathematics (etb) 27 2943-4955 Restricted to subscribers. https://ems.press/books This book describes the theory of profinite groups, from the basics of the theory to topics which are active areas of current research. It is the first textbook on profinite groups to make their use in studying residually finite groups via their profinite completions a central focus. The first part of the book gives the subject a firm theoretical underpinning from category theory and introduces profinite groups as objects worthy of study in their own right. The reader is not expected to have a background in category theory. The connection of a residually finite group to its profinite completion is explored in detail, with emphasis on various separability properties and profinite rigidity. The study of group cohomology is a key tool in the exploration of profinite groups. The central portion of this book gives a standalone first course in group cohomology before showing the modification of this theory for use with profinite groups. There is special emphasis on the unique features of profinite group cohomology such as Pontryagin duality and Sylow theory. Later chapters of the book collect together for the first time important results concerning the relation of the cohomology of a group to that of its profinite completion, and introduce the concept of an action of a profinite group on a profinite tree. This material aims to be a useful reference for researchers as well as a learning resource. Mathematics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory msc Limits, profinite groups msc Stone spaces (Boolean spaces) and related structures msc \(p\)-adic theory, local fields msc Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) msc Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations msc Groups acting on trees msc Residual properties and generalizations; residually finite groups msc Geometric group theory msc Cohomology of groups msc Covering spaces and low-dimensional topology msc https://ems.press/doi/10.4171/etb/27 cover image https://content.ems.press/assets/public/images/books/cover-290.png nam a22 5a 4500 10.4171/etm/37 DE-4084 2024-08-27 a fot 00| 0| cr nn mmmmamaa 240827e20240827gw fot 00| 0|eng d 9783985475797 10.4171/etm/37 doi DE-4084 PB bicssc 60-02 msc 58J65 msc 60B20 msc 60J65 msc Baudoin aut Stochastic Areas, Horizontal Brownian Motions, and Hypoelliptic Heat Kernels. EMS Press 2024 1 online resource (352 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Tracts in Mathematics (etm) 37 2943-5005 Restricted to subscribers. https://ems.press/books This book is a self-contained introduction to the theory of Brownian motions and heat kernels on matrix Lie groups and manifolds, with an emphasis on the study of area type functionals. It offers graduate students a systematic account of the subject and serves as a convenient resource and reference for more experienced mathematicians. The book emphasizes methods rather than results and takes the reader to the frontiers of current research, starting with carefully motivated examples and constructions. These aspects are supported by the inclusion of several bibliographic notes at the end of each chapter and appendices at the end of the book. This book can be used as a self-study guide for readers interested in the interplay between geometry and probability or as a textbook for a special topics course. Mathematics bicssc Research exposition (monographs, survey articles) pertaining to probability theory msc Diffusion processes and stochastic analysis on manifolds msc Random matrices (probabilistic aspects) msc Brownian motion msc Demni aut Wang aut https://ems.press/doi/10.4171/etm/37 cover image https://content.ems.press/assets/public/images/books/cover-292.png nam a22 5a 4500 10.4171/esiam/4 DE-4084 2024-09-05 a fot 00| 0| cr nn mmmmamaa 240905e20240905gw fot 00| 0|eng d 9783985475766 10.4171/esiam/4 doi DE-4084 PB bicssc 55M30 msc 68T40 msc 93C85 msc Farber edt Topology and AI ; Topological Aspects of Algorithms for Autonomous Motion. EMS Press 2024 1 online resource (400 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series in Industrial and Applied Mathematics (esiam) 4 2523-5095 Restricted to subscribers. https://ems.press/books The task of programming a machine to move autonomously and to make autonomous decisions is one of the major challenges of AI. The algorithms generating autonomous robot motions and autonomous decisions are sections of certain fibre bundles and their complexity and structure can be understood using tools of algebraic topology. The book gives an overview of the current achievements in the field of topological robotics concerned with motion algorithms, and in particular how their complexity depends on the topology of the configuration space of the system and the external conditions. The book is a collection of survey articles written by leading researchers in the fields of mathematics, engineering and computer science, with each chapter surveying a different theme or technique. Mathematics bicssc Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects) msc Artificial intelligence for robotics msc Automated systems (robots, etc.) in control theory msc González edt https://ems.press/doi/10.4171/esiam/4 cover image https://content.ems.press/assets/public/images/books/cover-293.png nam a22 5a 4500 10.4171/mlm/3 DE-4084 2024-09-07 a fot 00| 0| cr nn mmmmamaa 240907e20240907gw fot 00| 0|eng d 9783985475803 10.4171/mlm/3 doi DE-4084 PB bicssc 51-01 msc 51A50 msc 51E24 msc 51A45 msc 51B25 msc Van Maldeghem aut Polar Spaces. EMS Press 2024 1 online resource (182 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Münster Lectures in Mathematics (mlm) 3 2523-5249 Restricted to subscribers. https://ems.press/books Polar spaces are the natural geometries for the classical groups. Due to the stunning simplicity of an axiom system found by Buekenhout and Shult, they play a central role in incidence geometry and also appear as combinatorial objects in many disciplines such as discrete mathematics, graph theory, finite geometry and coding theory. They can also be viewed as a class of spherical Tits buildings and as such were classified by Jacques Tits - using pseudo-quadratic forms and octonion algebras. Polar spaces bridge the areas of group theory, algebra, combinatorics and incidence geometry. These lecture notes arose from a masters course in Ghent, Belgium, taught annually between 2010 and 2024. Besides many basic and general geometric properties of polar spaces, it contains a complete algebraic description of all polar spaces of rank at least 3, linking them with polarities in projective spaces. The discussion of the related classical groups is limited to the study of axial and central elations. The classification of top-thin polar spaces is included in detail. Triality in top-thin polar spaces of rank 4 is explained both geometrically and algebraically. The last chapter introduces parapolar spaces, which are geometric structures using polar spaces as building blocks. This opens the door for exploring geometries related to the exceptional groups. An appendix explains composition algebras, which are used to describe the so-called non-embeddable polar spaces and triality. Mathematics bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry msc Polar geometry, symplectic spaces, orthogonal spaces msc Buildings and the geometry of diagrams msc Incidence structures embeddable into projective geometries msc Lie geometries in nonlinear incidence geometry msc https://ems.press/doi/10.4171/mlm/3 cover image https://content.ems.press/assets/public/images/books/cover-295.png nam a22 5a 4500 10.4171/mlm/4 DE-4084 2024-12-03 a fot 00| 0| cr nn mmmmamaa 241203e20241203gw fot 00| 0|eng d 9783985475810 10.4171/mlm/4 doi DE-4084 PB bicssc 14-06 msc 14G22 msc 14G45 msc 11F85 msc 46S10 msc Hellmann edt Non-Archimedean Geometry and Eigenvarieties. EMS Press 2024 1 online resource (317 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Münster Lectures in Mathematics (mlm) 4 2523-5249 Restricted to subscribers. https://ems.press/books This book offers an introduction to the theory of adic spaces, with applications to the geometry of automorphic forms. It is comprised of expanded lecture notes for six mini-courses delivered by the contributing authors at the Spring School on Non-Archimedean Geometry and Eigenvarieties, held in March 2023 at Heidelberg University. The book is divided into two parts. The first part provides a focused, comprehensive and mostly self-contained introduction to the theory of adic spaces, with chapters contributed by John Bergdall, Katharina Hübner, and Christian Johansson. The second part demonstrates the theory through two key applications; perfectoid spaces, explained in a chapter by Ben Heuer, and eigenvarieties, covered in chapters by Judith Ludwig and James Newton. Designed for researchers and students with some background in algebraic geometry, this book serves as an accessible entry point into the theory. Numerous examples, illustrations, and carefully designed exercises are included throughout to help readers understand the concepts and build intuition before moving on to more advanced literature. Mathematics bicssc Proceedings, conferences, collections, etc. pertaining to algebraic geometry msc Rigid analytic geometry msc Perfectoid spaces and mixed characteristic msc \(p\)-adic theory, local fields msc Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis msc Ludwig edt Venjakob edt https://ems.press/doi/10.4171/mlm/4 cover image https://content.ems.press/assets/public/images/books/cover-297.png nam a22 5a 4500 10.4171/emm/12 DE-4084 2024-11-28 a fot 00| 0| cr nn mmmmamaa 241128e20241128gw fot 00| 0|eng d 9783985475827 10.4171/emm/12 doi DE-4084 PB bicssc PBP bicssc PBPD bicssc PHU bicssc 57-02 msc 57K16 msc 57K31 msc 57K30 msc 55R80 msc 57R20 msc 81Q30 msc Lescop aut Invariants of Links and 3-Manifolds from Graph Configurations. EMS Press 2024 1 online resource (587 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Monographs in Mathematics (emm) 12 2523-5206 Restricted to subscribers. https://ems.press/books This self-contained book explains how to count graph configurations to obtain topological invariants for 3-manifolds and links in these 3-manifolds, and it investigates the properties of the obtained invariants. The simplest of these invariants is the linking number of two disjoint knots in the ambient space described in the beginning of the book as the degree of a Gauss map. Mysterious knot invariants called quantum invariants were introduced in the mid-1980s, starting with the Jones polynomial. Witten explained how to obtain many of them from the perturbative expansion of the Chern-Simons theory. His physicist viewpoint led Kontsevich to a configuration-counting definition of topological invariants for the closed 3-manifolds where knots bound oriented compact surfaces. The book's first part shows in what sense an invariant previously defined by Casson for these manifolds counts embeddings of the theta graph. The second and third parts describe a configuration-counting invariant generalizing the above invariants. The fourth part shows the universality of with respect to some theories of finite-type invariants. The most sophisticated presented generalization of applies to small pieces of links in 3-manifolds called tangles. Its functorial properties and its behavior under cabling are used to describe the properties of . The book is written for graduate students and more advanced researchers interested in low-dimensional topology and knot theory. Mathematics bicssc Topology bicssc Algebraic topology bicssc Mathematical physics bicssc Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes msc Finite-type and quantum invariants, topological quantum field theories (TQFT) msc Invariants of 3-manifolds (including skein modules, character varieties) msc General topology of 3-manifolds msc Discriminantal varieties and configuration spaces in algebraic topology msc Characteristic classes and numbers in differential topology msc Feynman integrals and graphs; applications of algebraic topology and algebraic geometry msc https://ems.press/doi/10.4171/emm/12 cover image https://content.ems.press/assets/public/images/books/cover-296.png nam a22 5a 4500 10.4171/mems/16 DE-4084 2025-02-05 a fot 00| 0| cr nn mmmmamaa 250205e20250205gw fot 00| 0|eng d 9783985475858 10.4171/mems/16 doi DE-4084 PB bicssc PBKJ bicssc PBT bicssc PBWL bicssc PHU bicssc 60H15 msc 81T08 msc 60L40 msc 35L71 msc 35K15 msc Oh aut Stochastic Quantization of the -Model. EMS Press 2025 1 online resource (153 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 16 2747-9099 Open Access https://ems.press/books We study the construction of the ³₃-measure and complete the program on the (non-)construction of the focusing Gibbs measures, initiated by Lebowitz, Rose, and Speer [J. Statist. Phys. 50 (1988), no. 3-4, 657-687]. This problem turns out to be critical, exhibiting the following phase transition. In the weakly nonlinear regime, we prove normalizability of the ³₃-measure and show that it is singular with respect to the massive Gaussian free field. Moreover, we show that there exists a shifted measure with respect to which the ³₃-measure is absolutely continuous. In the strongly nonlinear regime, by further developing the machinery introduced by the authors, we establish non-normalizability of the ³₃-measure. Due to the singularity of the ³₃-measure with respect to the massive Gaussian free field, this non-normalizability part poses a particular challenge as compared to our previous works. In order to overcome this issue, we first construct a -finite version of the ³₃-measure and show that this measure is not normalizable. Furthermore, we prove that the truncated ³₃-measures have no weak limit in a natural space, even up to a subsequence. We also study the dynamical problem for the canonical stochastic quantization of the ³₃-measure, namely, the three-dimensional stochastic damped nonlinear wave equation with a quadratic nonlinearity forced by an additive space-time white noise ( the hyperbolic ³₃-model). By adapting the paracontrolled approach, in particular from the works by Gubinelli, Koch, and the first author [J. Eur. Math. Soc. 26 (2024), no. 3, 817-874] and by the authors [Mem. Amer. Math. Soc. 304 (2024), no. 1529], we prove almost sure global well-posedness of the hyperbolic ³₃-model and invariance of the Gibbs measure in the weakly nonlinear regime. In the globalization part, we introduce a new, conceptually simple and straightforward approach, where we directly work with the (truncated) Gibbs measure, using the Boué-Dupuis variational formula and ideas from theory of optimal transport. Mathematics bicssc Differential calculus & equations bicssc Probability & statistics bicssc Stochastics bicssc Mathematical physics bicssc Stochastic partial differential equations (aspects of stochastic analysis) msc Constructive quantum field theory msc Paracontrolled distributions and alternative approaches msc Second-order semilinear hyperbolic equations msc Initial value problems for second-order parabolic equations msc Okamoto aut Tolomeo aut https://ems.press/doi/10.4171/mems/16 cover image https://content.ems.press/assets/public/images/books/cover-301.png nam a22 5a 4500 10.4171/010 DE-4084 2004-12-10 a fot 00| 0| cr nn mmmmamaa 041210e20041210gw fot 00| 0|eng d 9783037195109 10.4171/010 doi DE-4084 PB bicssc PBKB bicssc PBKD bicssc PBM bicssc 26-01 msc 30F25 msc 30F45 msc 30F60 msc 32G15 msc 32Q45 msc 51-01 msc 51K05 msc 51K10 msc 51M09 msc 51M10 msc 51F99 msc 52-01 msc 52A07 msc 52A41 msc 53-01 msc 53C70 msc 54-01 msc 54E35 msc Papadopoulos aut Metric Spaces, Convexity and Nonpositive Curvature. EMS Press 2004 1 online resource (299 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda IRMA Lectures in Mathematics and Theoretical Physics (irma) 2523-5141 Restricted to subscribers. https://ems.press/books This book is about metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function satisfies a convexity condition. The book also contains a systematic introduction to the theory of geodesics in metric spaces, as well as a detailed presentation of some facets of convexity theory that are useful in the study of nonpositive curvature. The concepts and the techniques are illustrated by many examples from classical hyperbolic geometry and from the theory of Teichmüller spaces. The book is useful for students and researchers in geometry, topology and analysis. This book has appeared in a [second edition](https://doi.org/10.4171/132) in 2014. Mathematics bicssc Real analysis, real variables bicssc Complex analysis, complex variables bicssc Geometry bicssc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions msc Ideal boundary theory for Riemann surfaces msc Conformal metrics (hyperbolic, Poincaré, distance functions) msc Teichmüller theory for Riemann surfaces msc Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) msc Hyperbolic and Kobayashi hyperbolic manifolds msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry msc General theory of distance geometry msc Synthetic differential geometry msc Elementary problems in hyperbolic and elliptic geometries msc Hyperbolic and elliptic geometries (general) and generalizations msc Metric geometry msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to convex and discrete geometry msc Convex sets in topological vector spaces (aspects of convex geometry) msc Convex functions and convex programs in convex geometry msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry msc Direct methods (\(G\)-spaces of Busemann, etc.) msc Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general topology msc Metric spaces, metrizability msc https://ems.press/doi/10.4171/010 cover image https://content.ems.press/assets/public/images/books/cover-299.png nam a22 5a 4500 10.4171/061 DE-4084 2008-04-02 a fot 00| 0| cr nn mmmmamaa 080402e20080402gw fot 00| 0|eng d 9783037195611 10.4171/061 doi DE-4084 PB bicssc PBPH bicssc 58-02 msc 58B34 msc Khalkhali aut Basic Noncommutative Geometry. EMS Press 2008 1 online resource (239 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Lectures in Mathematics (elm) 2523-5184 Restricted to subscribers. https://ems.press/books *Basic Noncommutative Geometry* provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well. This book has appeared in a [second edition](https://doi.org/10.4171/128) in 2013. Mathematics bicssc Analytic topology bicssc Research exposition (monographs, survey articles) pertaining to global analysis msc Noncommutative geometry (à la Connes) msc https://ems.press/doi/10.4171/061 cover image https://content.ems.press/assets/public/images/books/cover-298.png nam a22 5a 4500 10.4171/mems/15 DE-4084 2025-02-05 a fot 00| 0| cr nn mmmmamaa 250205e20250205gw fot 00| 0|eng d 9783985475865 10.4171/mems/15 doi DE-4084 PB bicssc PBMW bicssc 14N35 msc 14A21 msc 14D20 msc 14D23 msc 14T99 msc Abramovich aut Punctured Logarithmic Maps. EMS Press 2025 1 online resource (164 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 15 2747-9099 Open Access https://ems.press/books We introduce a variant of stable logarithmic maps, which we call *punctured logarithmic maps*. They allow an extension of logarithmic Gromov-Witten theory in which marked points have a negative order of tangency with boundary divisors. As a main application we develop a gluing formalism which reconstructs stable logarithmic maps and their virtual cycles without expansions of the target, with tropical geometry providing the underlying combinatorics. Punctured Gromov-Witten invariants also play a pivotal role in the intrinsic construction of mirror partners by the last two authors, conjecturally relating to symplectic cohomology, and in the logarithmic gauged linear sigma model in work of Qile Chen, Felix Janda and Yongbin Ruan. Mathematics bicssc Algebraic geometry bicssc Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) msc Logarithmic algebraic geometry, log schemes msc Algebraic moduli problems, moduli of vector bundles msc Stacks and moduli problems msc Tropical geometry msc Chen aut Gross aut Siebert aut https://ems.press/doi/10.4171/mems/15 cover image https://content.ems.press/assets/public/images/books/cover-300.png nam a22 5a 4500 10.4171/mems/17 DE-4084 2025-02-05 a fot 00| 0| cr nn mmmmamaa 250205e20250205gw fot 00| 0|eng d 9783985475872 10.4171/mems/17 doi DE-4084 PB bicssc PBP bicssc 57K41 msc 57R57 msc 57R58 msc Sasahira aut Seiberg-Witten Floer Spectra for b >0. EMS Press 2025 1 online resource (151 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 17 2747-9099 Open Access https://ems.press/books The Seiberg-Witten Floer spectrum is a stable homotopy refinement of the monopole Floer homology of Kronheimer and Mrowka. The Seiberg-Witten Floer spectrum was defined by Manolescu for closed, spin 3-manifolds with b₁ 0 in an ¹-equivariant stable homotopy category and has been producing interesting topological applications. Lidman and Manolescu showed that the ¹-equivariant homology of the spectrum is isomorphic to the monopole Floer homology. For closed spin 3-manifolds with ₁() > 0, there are analytic and homotopy-theoretic difficulties in defining the Seiberg-Witten Floer spectrum. In this memoir, we address the difficulties and construct the Seiberg-Witten Floer spectrum for , provided that the first Chern class of the spin structure is torsion and that the triple-cup product on ¹(;) vanishes. We conjecture that its ¹-equivariant homology is isomorphic to the monopole Floer homology. For a 4-dimensional spin cobordism between ₀ and ₁, we define the Bauer-Furuta map on these new spectra of ₀ and ₁, which is conjecturally a refinement of the relative Seiberg-Witten invariant of . As an application, for a compact spin 4-manifold with boundary , we prove a 10/8-type inequality for which is written in terms of the intersection form of and an invariant () of . In addition, we compute the Seiberg-Witten Floer spectrum for some 3-manifolds. Mathematics bicssc Topology bicssc Invariants of 4-manifolds (including Donaldson and Seiberg-Witten invariants) msc Applications of global analysis to structures on manifolds msc Floer homology msc Stoffregen aut https://ems.press/doi/10.4171/mems/17 cover image https://content.ems.press/assets/public/images/books/cover-302.png nam a22 5a 4500 10.4171/mems/19 DE-4084 2025-03-20 a fot 00| 0| cr nn mmmmamaa 250320e20250320gw fot 00| 0|eng d 9783985475889 10.4171/mems/19 doi DE-4084 PB bicssc PBF bicssc PBMW bicssc 13J07 msc 14F30 msc 14G22 msc Zavyalov aut Almost Coherent Modules and Almost Coherent Sheaves. EMS Press 2025 1 online resource (314 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 19 2747-9099 Open Access https://ems.press/books We extend the theory of almost coherent modules that was introduced in *Almost ring theory* by Gabber and Ramero (2003). Then we globalize it by developing a new theory of almost coherent sheaves on schemes and on a class of nice formal schemes. We show that these sheaves satisfy many properties similar to usual coherent sheaves, i.e., the amost proper mapping theorem, the formal GAGA, etc. We also construct an almost version of the Grothendieck twisted image functor  and verify its properties. Lastly, we study sheaves of -adic nearby cycles on admissible formal models of rigid-analytic varieties and show that these sheaves provide examples of almost coherent sheaves. This gives a new proof of the finiteness result for étale cohomology of proper rigid-analytic varieties obtained before in Scholze's work *-adic Hodge theory for rigid-analytic varieties* (2013). Mathematics bicssc Algebra bicssc Algebraic geometry bicssc Analytical algebras and rings msc \(p\)-adic cohomology, crystalline cohomology msc Rigid analytic geometry msc https://ems.press/doi/10.4171/mems/19 cover image https://content.ems.press/assets/public/images/books/cover-306.png nam a22 5a 4500 10.4171/mems/20 DE-4084 2025-05-05 a fot 00| 0| cr nn mmmmamaa 250505e20250505gw fot 00| 0|eng d 9783985475902 10.4171/mems/20 doi DE-4084 PB bicssc PBG bicssc PBH bicssc 11F72 msc 20G35 msc 22E55 msc Labesse aut La formule des traces tordue pour un corps global de caractéristique p>0 (The Twisted Trace Formula for a Global Field of Characteristic p>0). EMS Press 2025 1 online resource (219 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 20 2747-9099 Open Access https://ems.press/books Résumé Dans ce travail nous adaptons au cas d'un corps global de caractéristique positive, c'est-à-dire un corps de fonctions sur un corps fini , les résultats prouvés pour un corps de nombres dans le livre de Labesse-Waldspurger *La formule des traces tordue d'après le Friday Morning Seminar*. En d'autres termes, nous établissons la formule des traces pour un -espace tordu où est un groupe réductif connexe défini sur . C'est une première étape vers la forme stabilisée de la formule des traces tordue, nécessaire pour la plupart des applications, qui, elle, est l'objet de travaux en cours. Abstract In this work, the authors adapt to the case of a global field of positive characteristic, that is, a field of functions over a finite field , the results proved for a number field in Labesse-Waldspurger's book _La formule des traces tordue d'après le Friday Morning Seminar_. In other words, the authors establish the trace formula for a twisted -space , where is a connected reductive group defined over . This is a first step towards the stabilized form of the twisted trace formula, necessary for most applications, which is the subject of ongoing work. Mathematics bicssc Groups & group theory bicssc Number theory bicssc Spectral theory; trace formulas (e.g., that of Selberg) msc Linear algebraic groups over adèles and other rings and schemes msc Representations of Lie and linear algebraic groups over global fields and adèle rings msc Lemaire aut https://ems.press/doi/10.4171/mems/20 cover image https://content.ems.press/assets/public/images/books/cover-307.png nam a22 5a 4500 10.4171/mems/18 DE-4084 2025-02-15 a fot 00| 0| cr nn mmmmamaa 250215e20250215gw fot 00| 0|eng d 9783985475919 10.4171/mems/18 doi DE-4084 PB bicssc PBK bicssc PBPH bicssc PHU bicssc 58B32 msc 58B34 msc 46L89 msc 46L30 msc 81R60 msc Kaad aut The Quantum Metric Structure of Quantum SU(2). EMS Press 2025 1 online resource (127 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 18 2747-9099 Open Access https://ems.press/books We introduce a two parameter family of Dirac operators on quantum SU(2) and analyse their properties from the point of view of non-commutative metric geometry. It is shown that these Dirac operators give rise to compact quantum metric structures, and that the corresponding two parameter family of compact quantum metric spaces varies continuously in Rieffel's quantum Gromov-Hausdorff distance. This continuity result includes the classical case where we recover the round 3-sphere up to a global scaling factor on the metric. Our main technical tool is a quantum SU(2) analogue of the Berezin transform, together with its associated fuzzy approximations, the analysis of which also leads to a systematic way of approximating Lipschitz operators by means of polynomial expressions in the generators. Mathematics bicssc Calculus & mathematical analysis bicssc Analytic topology bicssc Mathematical physics bicssc Geometry of quantum groups msc Noncommutative geometry (à la Connes) msc Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory msc States of selfadjoint operator algebras msc Noncommutative geometry in quantum theory msc Kyed aut https://ems.press/doi/10.4171/mems/18 cover image https://content.ems.press/assets/public/images/books/cover-303.png nam a22 5a 4500 10.4171/emm/13 DE-4084 2025-02-26 a fot 00| 0| cr nn mmmmamaa 250226e20250226gw fot 00| 0|eng d 9783985475896 10.4171/emm/13 doi DE-4084 PB bicssc PBKQ bicssc PBU bicssc 49-02 msc 49Q20 msc 49J45 msc 49N60 msc De Lellis aut The Regularity Theory for the Mumford-Shah Functional on the Plane. EMS Press 2025 1 online resource (266 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Monographs in Mathematics (emm) 13 2523-5206 Restricted to subscribers. https://ems.press/books This book provides a thorough and up-to-date account of the state of art of the regularity theory for minimizers of the Mumford-Shah functional of image segmentation in the 2-dimensional setting. Starting with some classical preliminary results, which settle the issue of existence of minimizing couples (,), the structure of the set is then analyzed by using -regularity theorems. Several consequences of the latter are also investigated, in particular leading to different characterizations of the Mumford-Shah conjecture. The proofs are given with full details, often revisiting the relevant literature and introducing new arguments. Mathematics bicssc Calculus of variations bicssc Optimization bicssc Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control msc Variational problems in a geometric measure-theoretic setting msc Methods involving semicontinuity and convergence; relaxation msc Regularity of solutions in optimal control msc Focardi aut https://ems.press/doi/10.4171/emm/13 cover image https://content.ems.press/assets/public/images/books/cover-304.png nam a22 5a 4500 10.4171/ecr/20 DE-4084 2025-03-03 a fot 10| 0| cr nn mmmmamaa 250303e20250303gw fot 10| 0|eng d 9783985475841 10.4171/ecr/20 doi DE-4084 PB bicssc PBH bicssc 11-06 msc 11G40 msc 11M38 msc 11G09 msc 11R23 msc 11R29 msc 11R42 msc 11R59 msc 11F80 msc Bullach edt Arithmetic of L-Functions ; Proceedings of an International Conference held at ICMAT, Madrid, May 2023. EMS Press 2025 1 online resource (366 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 20 2523-5168 Restricted to subscribers. https://ems.press/books This volume brings together research and survey articles in algebraic number theory and arithmetic geometry. All of them share as a general theme the mysterious connections between special values of -functions and algebraic invariants of Galois representations. These relationships are explored primarily through the lenses of Iwasawa theory and other Galois-equivariant points of view. The topics covered include the Galois module structure of ideal class groups, reciprocity laws in Iwasawa theory, Euler systems, -adic -functions, and étale cohomology - each of which has had a remarkable importance in the study of -adic Galois representations over the last few decades. In addition, the final chapters of this volume serve as an introduction to the emerging subject of special -values in positive characteristic. This is a new direction in the general area of global function field arithmetic that is concerned with the invariants of Galois representations valued in positive characteristic, as provided by Drinfeld modules or -modules. Serving as the proceedings of an international conference held at ICMAT (Madrid) in May 2023, this volume is a useful resource for important techniques and approaches, as well as a source of concrete results and bibliographic references. It is of interest both to established researchers and to graduate students interested in algebraic number theory or in arithmetic geometry. Mathematics bicssc Number theory bicssc Proceedings, conferences, collections, etc. pertaining to number theory msc \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture msc Zeta and \(L\)-functions in characteristic \(p\) msc Drinfel'd modules; higher-dimensional motives, etc. msc Iwasawa theory msc Class numbers, class groups, discriminants msc Zeta functions and \(L\)-functions of number fields msc Zeta functions and \(L\)-functions of function fields msc Galois representations msc Macías Castillo edt https://ems.press/doi/10.4171/ecr/20 cover image https://content.ems.press/assets/public/images/books/cover-305.png nam a22 5a 4500 10.4171/hem/14 DE-4084 2025-08-25 a fot 00| 0| cr nn mmmmamaa 250825e20250825gw fot 00| 0|eng d 9783985475926 10.4171/hem/14 doi DE-4084 PB bicssc PBMP bicssc PBX bicssc PHU bicssc 53-03 msc 83-03 msc 01A60 msc 83C05 msc 53C05 msc 53C80 msc 53A45 msc Tazzioli aut From Differential Geometry to Relativity ; Levi-Civitas Lectures on the Absolute Differential Calculus, 1925-1928. EMS Press 2025 1 online resource (535 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Heritage of European Mathematics (hem) 14 2523-5222 Restricted to subscribers. https://ems.press/books This book examines Levi-Civitas lectures on tensor calculus as a lens to illuminate key aspects of his scientific legacy. It highlights the deep interplay between his teaching and research, particularly in tensor calculus, differential geometry, and relativity, as well as his role as a mentor at the University of Rome. More broadly, it traces the history of Riemannian differential geometry from roughly 1870 to 1930. Key themes emerge: the influence of the Italian mathematical tradition in Levi-Civitas work on tensor calculus, the intrinsic link between analysis, geometry, and relativity in his work, and his pedagogical approach, which incorporates physics and geometric intuition to extend mathematical results. The book also explores his collaborations with Enrico Fermi and Enrico Persico, shedding light on the Via Panisperna group during a pivotal period in theoretical physics. Levi-Civitas treatise became a foundational text in absolute differential calculus, essential for physicists mastering tensor calculus in Einsteins theories. Drawing extensively from his archives - preserved at the Archivio Storico dellAccademia Nazionale dei Lincei in Rome and within the Ceccherini-Silberstein family - the book offers fresh insights into his personal, scientific, and academic life. His correspondence reveals his far-reaching influence, spanning students in Rome, international scholars, Rockefeller fellows, and colleagues inspired by his ideas and mentorship. Mathematics bicssc Differential & Riemannian geometry bicssc History of mathematics bicssc Mathematical physics bicssc History of differential geometry msc History of relativity and gravitational theory msc History of mathematics in the 20th century msc Einstein's equations (general structure, canonical formalism, Cauchy problems) msc Connections (general theory) msc Applications of global differential geometry to the sciences msc Differential geometric aspects in vector and tensor analysis msc https://ems.press/doi/10.4171/hem/14 cover image https://content.ems.press/assets/public/images/books/cover-311.png nam a22 5a 4500 10.4171/emm/14 DE-4084 2025-07-29 a fot 00| 0| cr nn mmmmamaa 250729e20250729gw fot 00| 0|eng d 9783985475933 10.4171/emm/14 doi DE-4084 PB bicssc PBMP bicssc 53-02 msc 53D40 msc 53D37 msc 53D42 msc Venugopalan aut Tropical Fukaya Algebras. EMS Press 2025 1 online resource (377 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Monographs in Mathematics (emm) 14 2523-5206 Restricted to subscribers. https://ems.press/books In this book, we explore the degeneration of pseudoholomorphic disks bounding a Lagrangian in a symplectic manifold in the large complex structure limit corresponding to a multiple cut. The limit objects, called broken disks, have underlying tropical graphs which in the case of pseudoholomorphic spheres were studied by Brett Parker. In particular, we study the limit of the Fukaya algebra of a Lagrangian submanifold, which is an  algebra whose higher composition maps involve counts of pseudoholomorphic disks. The goal of the book is to prove an  homotopy equivalence between the ordinary Fukaya algebra of a Lagrangian and a tropical version of the Fukaya algebra defined via counts of broken disks with rigid tropical graphs. The exposition is self-contained and includes details of the transversality scheme. Various computations of disk potentials of Lagrangian submanifolds, such as those in cubic surfaces and flag varieties, are included. Mathematics bicssc Differential & Riemannian geometry bicssc Research exposition (monographs, survey articles) pertaining to differential geometry msc Symplectic aspects of Floer homology and cohomology msc Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category msc Symplectic field theory; contact homology msc Woodward aut https://ems.press/doi/10.4171/emm/14 cover image https://content.ems.press/assets/public/images/books/cover-310.png nam a22 5a 4500 10.4171/ecr/21 DE-4084 2025-10-03 a fot 10| 0| cr nn mmmmamaa 251003e20251003gw fot 10| 0|eng d 9783985475834 10.4171/ecr/21 doi DE-4084 PB bicssc PBF bicssc 16-06 msc 16G10 msc 16E35 msc 18G25 msc Angeleri Hügel edt Representations of Algebras and Related Topics ; Proceedings of the Workshop and the 20th International Conference on Representations of Algebras, ICRA 2022, Montevideo, Uruguay and Buenos Aires, Argentina, 3-12 August 2022. EMS Press 2025 1 online resource (508 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 21 2523-5168 Restricted to subscribers. https://ems.press/books This volume presents a collection of articles devoted to representations of algebras and related topics. Distinguished experts in this field presented their work at the International Conference on Representations of Algebras which took place in Montevideo and Buenos Aires in 2022. The book reflects recent trends in the representation theory of algebras and its interactions with other central branches of mathematics. There are fourteen expository survey papers, written by leading experts in the field. This collection is addressed to researchers and graduate students in algebra as well as to a broader mathematical audience. Researchers of representation theory will find in this volume interesting and stimulating contributions to the development of the subject. Mathematics bicssc Algebra bicssc Proceedings, conferences, collections, etc. pertaining to associative rings and algebras msc Representations of associative Artinian rings msc Derived categories and associative algebras msc Relative homological algebra, projective classes (category-theoretic aspects) msc Keller edt Redondo edt Solotar edt https://ems.press/doi/10.4171/ecr/21 cover image https://content.ems.press/assets/public/images/books/cover-312.png nam a22 5a 4500 10.4171/nnu90 DE-4084 2025-07-22 a fot 00| 0| cr nn mmmmamaa 250722e20250722gw fot 00| 0|eng d 9783985475940 10.4171/nnu90 doi DE-4084 PB bicssc PBKJ bicssc PBKQ bicssc PBU bicssc PBMP bicssc PHU bicssc 35-06 msc 35B27 msc 35B32 msc 35B36 msc 35B65 msc 35J87 msc 35K10 msc 35K58 msc 35R11 msc 35R35 msc 35R37 msc 49J20 msc 53A04 msc 76B25 msc Apushkinskaya edt Friends in Partial Differential Equations ; The Nina N. Uraltseva 90th Anniversary Volume. EMS Press 2025 1 online resource (389 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Restricted to subscribers. https://ems.press/books This volume is dedicated to Nina Nikolaevna Uraltseva on the occasion of her 90th birthday. It collects contributions by her numerous colleagues and friends sharing with her research interests in linear and quasilinear elliptic and parabolic equations, degenerate and geometric equations, variational inequalities, and free boundary problems. In brief, the topics covered include regularity for transmission systems, bifurcation of solitary waves, parabolic equations with Morrey lower-order coefficients, mesoscopic modeling of optimal transportation networks, Sobolev regularity in nonlinear elliptic problems, planar loops with prescribed curvature, interface behavior for the solutions of free boundary problems, a multi-phase Stefan problem, homogenization of nonlocal convolution-type operators, an obstacle-type problem for the -Laplacian with the fractional gradient, scalar variational problems with maximal singular sets, bifurcations in the Lotka-Volterra competition model, and the Dirichlet-area minimisation problem. In addition, the volume contains a description of Uraltsevas main contributions to mathematics and the mathematical community. Mathematics bicssc Differential calculus & equations bicssc Calculus of variations bicssc Optimization bicssc Differential & Riemannian geometry bicssc Mathematical physics bicssc Proceedings, conferences, collections, etc. pertaining to partial differential equations msc Homogenization in context of PDEs; PDEs in media with periodic structure msc Bifurcations in context of PDEs msc Pattern formations in context of PDEs msc Smoothness and regularity of solutions to PDEs msc Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators msc Second-order parabolic equations msc Semilinear parabolic equations msc Fractional partial differential equations msc Free boundary problems for PDEs msc Moving boundary problems for PDEs msc Existence theories for optimal control problems involving partial differential equations msc Curves in Euclidean and related spaces msc Solitary waves for incompressible inviscid fluids msc Laptev edt Nazarov edt Shahgholian edt https://ems.press/doi/10.4171/nnu90 cover image https://content.ems.press/assets/public/images/books/cover-309.png nam a22 5a 4500 10.4171/mems/21 DE-4084 2025-06-28 a fot 00| 0| cr nn mmmmamaa 250628e20250628gw fot 00| 0|eng d 9783985475957 10.4171/mems/21 doi DE-4084 PB bicssc PBH bicssc 11F55 msc 11F50 msc Ma aut Vector-Valued Orthogonal Modular Forms. EMS Press 2025 1 online resource (155 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 21 2747-9099 Open Access https://ems.press/books This memoir is devoted to the theory of vector-valued modular forms for orthogonal groups of signature (2, ). Our purpose is multi-layered: (1) to lay a foundation of the theory of vector-valued orthogonal modular forms; (2) to develop some aspects of the theory in more depth such as geometry of the Siegel operators, filtrations associated to 1-dimensional cusps, decomposition of vector-valued Jacobi forms, square integrability etc; and (3) as applications derive several types of vanishing theorems for vector-valued modular forms of small weight. Our vanishing theorems imply in particular vanishing of holomorphic tensors of degree less than /2-1 on orthogonal modular varieties, which is optimal as a general bound. The fundamental ingredients of the theory are the two Hodge bundles. The first is the Hodge line bundle which already appears in the theory of scalar-valued modular forms. The second Hodge bundle emerges in the vector-valued theory and plays a central role. It corresponds to the non-abelian part (,) of the maximal compact subgroup of (2,). The main focus of this monograph is centered around the properties and the role of the second Hodge bundle in the theory of vector-valued orthogonal modular forms. Mathematics bicssc Number theory bicssc Other groups and their modular and automorphic forms (several variables) msc Jacobi forms msc https://ems.press/doi/10.4171/mems/21 cover image https://content.ems.press/assets/public/images/books/cover-308.png nam a22 5a 4500 10.4171/mems/25 DE-4084 2025-10-21 a fot 00| 0| cr nn mmmmamaa 251021e20251021gw fot 00| 0|eng d 9783985475988 10.4171/mems/25 doi DE-4084 PB bicssc PBKJ bicssc PHU bicssc 35M12 msc 76D10 msc 35K65 msc 35R35 msc Dalibard aut Linear and Nonlinear Parabolic Forward-Backward Problems. EMS Press 2025 1 online resource (148 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 25 2747-9099 Open Access https://ems.press/books The purpose of this memoir is to investigate the well-posedness of several linear and nonlinear equations with a parabolic forward-backward structure, and to highlight the similarities and differences between them. The epitomal linear example will be the stationary Kolmogorov equation   in a rectangle. We first prove that this equation admits a finite number of singular solutions, of which we provide an explicit construction. Hence, the solutions to the Kolmogorov equation associated with a smooth source term are regular if and only if satisfies a finite number of orthogonality conditions. We then extend this theory to a Vlasov-Poisson-Fokker-Planck system, and to two quasilinear equations: the Burgers-type equation   in the vicinity of the linear shear flow, and the Prandtl system in the vicinity of a recirculating solution, close to the line where the horizontal velocity changes sign. We therefore revisit part of a recent work by Iyer and Masmoudi. For the two latter quasilinear equations, we introduce a geometric change of variables which simplifies the analysis. In these new variables, the linear differential operator is very close to the Kolmogorov operator  . Stepping on the linear theory, we prove existence and uniqueness of regular solutions for data within a manifold of finite codimension, corresponding to some nonlinear orthogonality conditions. Mathematics bicssc Differential calculus & equations bicssc Mathematical physics bicssc Boundary value problems for PDEs of mixed type msc Boundary-layer theory, separation and reattachment, higher-order effects msc Degenerate parabolic equations msc Free boundary problems for PDEs msc Marbach aut Rax aut https://ems.press/doi/10.4171/mems/25 cover image https://content.ems.press/assets/public/images/books/cover-316.png nam a22 5a 4500 10.4171/mems/22 DE-4084 2025-10-07 a fot 00| 0| cr nn mmmmamaa 251007e20251007gw fot 00| 0|eng d 9783985475995 10.4171/mems/22 doi DE-4084 PB bicssc PBKJ bicssc PHU bicssc 76E05 msc 35P15 msc Almog aut On the Stability of Symmetric Flows in a Two-Dimensional Channel. EMS Press 2025 1 online resource (212 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 22 2747-9099 Open Access https://ems.press/books We consider the stability of symmetric flows in a two-dimensional channel (including the Poiseuille flow). In 2015 Grenier, Guo, and Nguyen have established instability of these flows in a particular region of the parameter space, affirming formal asymptotics results from the 1940s. We prove that these flows are stable outside this region in parameter space. More precisely we show that the Orr-Sommerfeld operator ( d/d + i( + i)) (d/d ) i which is defined on () { ⁴(0,1) | (0) ⁽³⁾(0) 0 and (1) (1) 0 } is bounded on the half-plane 0 for ^1/10 or ^1/6. Mathematics bicssc Differential calculus & equations bicssc Mathematical physics bicssc Parallel shear flows in hydrodynamic stability msc Estimates of eigenvalues in context of PDEs msc Helffer aut https://ems.press/doi/10.4171/mems/22 cover image https://content.ems.press/assets/public/images/books/cover-313.png nam a22 5a 4500 10.4171/mems/26 DE-4084 2025-12-06 a fot 00| 0| cr nn mmmmamaa 251206e20251206gw fot 00| 0|eng d 9783985475971 10.4171/mems/26 doi DE-4084 PB bicssc PBKJ bicssc 35A01 msc 35Q83 msc 35Q30 msc 35Q35 msc Ertzbischoff aut On Well-Posedness for Thick Spray Equations. EMS Press 2025 1 online resource (180 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 26 2747-9099 Open Access https://ems.press/books In this memoir, we prove the local-in-time well-posedness of thick spray equations in Sobolev spaces, for initial data satisfying a Penrose-type stability condition. This system is a coupling between particles described by a kinetic equation and a surrounding fluid governed by compressible Navier-Stokes equations. In the thick spray regime, the volume fraction of the dispersed phase is not negligible compared to that of the fluid. We identify a suitable stability condition bearing on the initial data that provides estimates without loss, ensuring that the system is well posed. This condition coincides with a Penrose condition appearing in earlier works on singular Vlasov equations. We also rely on crucial new estimates for averaging operators. Our approach allows us to treat many variants of the model, such as collisions in the kinetic equation, non-barotropic fluid or density-dependent drag force. Mathematics bicssc Differential calculus & equations bicssc Existence problems for PDEs: global existence, local existence, non-existence msc Vlasov equations msc Navier-Stokes equations msc PDEs in connection with fluid mechanics msc Han-Kwan aut https://ems.press/doi/10.4171/mems/26 cover image https://content.ems.press/assets/public/images/books/cover-317.png nam a22 5a 4500 10.4171/mems/24 DE-4084 2025-10-09 a fot 00| 0| cr nn mmmmamaa 251009e20251009gw fot 00| 0|eng d 9783985476008 10.4171/mems/24 doi DE-4084 PB bicssc PBF bicssc PBG bicssc PBH bicssc PBK bicssc PBMW bicssc 11S25 msc 14G22 msc 22E50 msc 46S10 msc 13J05 msc 13F25 msc 12G05 msc 11R23 msc Schneider aut Reciprocity Laws for (_L, _L)-Modules over Lubin-Tate Extensions. EMS Press 2025 1 online resource (194 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 24 2747-9099 Open Access https://ems.press/books In the Lubin-Tate setting we study pairings for analytic (_L, _L)-modules and prove an abstract reciprocity law which then implies a relation between the analogue of Perrin-Rious big exponential map as developed by Berger and Fourquaux and a -adic regulator map whose construction relies on the theory of Kisin-Ren modules generalising the concept of Wach modules to the Lubin-Tate situation. Mathematics bicssc Algebra bicssc Groups & group theory bicssc Number theory bicssc Calculus & mathematical analysis bicssc Algebraic geometry bicssc Galois cohomology msc Rigid analytic geometry msc Representations of Lie and linear algebraic groups over local fields msc Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis msc Power series rings msc Formal power series rings msc Galois cohomology msc Iwasawa theory msc Venjakob aut https://ems.press/doi/10.4171/mems/24 cover image https://content.ems.press/assets/public/images/books/cover-315.png nam a22 5a 4500 10.4171/mems/23 DE-4084 2025-10-07 a fot 00| 0| cr nn mmmmamaa 251007e20251007gw fot 00| 0|eng d 9783985476015 10.4171/mems/23 doi DE-4084 PB bicssc PBH bicssc PBK bicssc PBV bicssc 11T22 msc 05C05 msc 05C25 msc 05C60 msc 11A07 msc 37P25 msc Bors aut Functional Graphs of Generalized Cyclotomic Mappings of Finite Fields. EMS Press 2025 1 online resource (270 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 23 2747-9099 Open Access https://ems.press/books The functional graph of a function : is the directed graph with vertex set , the edges of which are of the form () for . Functional graphs are studied because they allow one to understand the behavior of under iteration (i.e., to understand the discrete dynamical system (,)), which has various applications, especially when is a finite field . This memoir is an extensive study of the functional graphs of so-called index d generalized cyclotomic mappings of , which are a natural and manageable generalization of monomial functions. We provide both theoretical results on the structure of their functional graphs and Las Vegas algorithms for solving fundamental problems, such as parametrizing the connected components of the functional graph by representative vertices, or describing the structure of a connected component given by a representative vertex. The complexity of these algorithms is analyzed in detail, and we make the point that for fixed index d and most prime powers (in the sense of asymptotic density), suitable implementations of these algorithms have an expected runtime that is polynomial in log on quantum computers, whereas their expected runtime is subexponential in log on a classical computer. We also discuss four special cases in which one can devise Las Vegas algorithms with this kind of complexity behavior over most finite fields that solve the graph isomorphism problem for functional graphs of generalized cyclotomic mappings. Mathematics bicssc Number theory bicssc Calculus & mathematical analysis bicssc Combinatorics & graph theory bicssc Cyclotomy msc Trees msc Graphs and abstract algebra (groups, rings, fields, etc.) msc Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) msc Congruences; primitive roots; residue systems msc Dynamical systems over finite ground fields msc Panario aut Wang aut https://ems.press/doi/10.4171/mems/23 cover image https://content.ems.press/assets/public/images/books/cover-314.png nam a22 5a 4500 10.4171/ecr/22 DE-4084 2025-12-10 a fot 00| 0| cr nn mmmmamaa 251210e20251210gw fot 00| 0|eng d 9783985475964 10.4171/ecr/22 doi DE-4084 PBMW bicssc 14-06 msc Bürgisser edt Varieties, Polyhedra, Computation. EMS Press 2025 1 online resource (602 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda EMS Series of Congress Reports (ecr) 22 2523-5168 Restricted to subscribers. https://ems.press/books This volume collects contributions from the thematic Einstein semester on algebraic geometry that took place in the winter semester 2019/2020 in Berlin, Germany and was devoted to interactions of algebraic geometry with other fields as well as applications with a potential impact from/on algebraic geometric methods. Following the semester's topics, the present volume includes a selection of important survey and research articles by leading researchers in the field, which will be of interest to both young and experienced mathematicians working in algebraic geometry and its applications. Algebraic geometry bicssc Proceedings, conferences, collections, etc. pertaining to algebraic geometry msc Farkas edt Haase edt https://ems.press/doi/10.4171/ecr/22 cover image https://content.ems.press/assets/public/images/books/cover-318.png nam a22 5a 4500 10.4171/mems/27 DE-4084 2026-03-10 a fot 00| 0| cr nn mmmmamaa 260310e20260310gw fot 00| 0|eng d 9783985476022 10.4171/mems/27 doi DE-4084 PB bicssc PBV bicssc PBT bicssc PBWL bicssc 60F17 msc 05C10 msc Bettinelli aut Compact Brownian Surfaces II ; Orientable Surfaces. EMS Press 2026 1 online resource (135 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Memoirs of the European Mathematical Society (mems) 27 2747-9099 Open Access https://ems.press/books Fix an arbitrary compact orientable surface with a boundary and consider a uniform bipartite random quadrangulation of this surface with faces and boundary component lengths of order or of lower order. Endow this quadrangulation with the usual graph metric renormalized by n/, mark it on each boundary component, and endow it with the counting measure on its vertex set renormalized by , as well as the counting measure on each boundary component renormalized by n/. We show that, as goes to infinity, this random marked measured metric space converges in distribution for the Gromov-Hausdorff-Prokhorov topology, toward a random limiting marked measured metric space called a *Brownian surface*. This extends known convergence results of uniform random planar quadrangulations with at most one boundary component toward the *Brownian sphere* and toward the *Brownian disk*, by considering the case of quadrangulations on general compact orientable surfaces. Our approach consists in cutting a Brownian surface into elementary pieces that are naturally related to the Brownian sphere and the Brownian disk and their noncompact analogs, the Brownian plane and the Brownian half-plane, and to prove convergence results for these elementary pieces, which are of independent interest. Mathematics bicssc Combinatorics & graph theory bicssc Probability & statistics bicssc Stochastics bicssc Functional limit theorems; invariance principles msc Planar graphs; geometric and topological aspects of graph theory msc Miermont aut https://ems.press/doi/10.4171/mems/27 cover image https://content.ems.press/assets/public/images/books/cover-319.png