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10.4171/004
DE-4084
2004-01-31
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DE-4084
PB
bicssc
53C05
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53C07
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58J32
msc
Wehrheim
aut
Uhlenbeck Compactness.
EMS Press
2004
1 online resource (219 pages)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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.
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
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nam a22 5a 4500
10.4171/063
DE-4084
2008-06-26
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9783037195635
10.4171/063
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DE-4084
PBMP
bicssc
53D40
msc
32Q65
msc
53D12
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16E45
msc
Seidel
aut
Fukaya Categories and Picard-Lefschetz Theory.
EMS Press
2008
1 online resource (334 pages)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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nam a22 5a 4500
10.4171/000
DE-4084
2003-12-15
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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)
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EMS Monographs in Mathematics (emm)
2523-5206
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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
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nam a22 5a 4500
10.4171/003
DE-4084
2004-05-31
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9783037195031
10.4171/003
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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)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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nam a22 5a 4500
10.4171/001
DE-4084
2004-02-15
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9783037195017
10.4171/001
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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)
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EMS Textbooks in Mathematics (etb)
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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
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nam a22 5a 4500
10.4171/002
DE-4084
2004-02-28
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9783037195024
10.4171/002
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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)
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ESI Lectures in Mathematics and Physics (esi)
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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
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nam a22 5a 4500
10.4171/005
DE-4084
2008-02-05
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9783037195055
10.4171/005
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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)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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nam a22 5a 4500
10.4171/006
DE-4084
2004-10-25
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9783037195062
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PBKJ
bicssc
53Axx
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58Jxx
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Chang
aut
Non-linear Elliptic Equations in Conformal Geometry.
EMS Press
2004
1 online resource (100 pages)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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nam a22 5a 4500
10.4171/132
DE-4084
2014-01-18
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9783037196328
10.4171/132
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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)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
6
2523-5141
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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.
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
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nam a22 5a 4500
10.4171/009
DE-4084
2005-06-30
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PB
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Laptev
edt
European Congress of Mathematics ;
Stockholm, June 27 - July 2, 2004.
EMS Press
2005
1 online resource (897 pages)
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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
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10.4171/012
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2005-05-31
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9783037195123
10.4171/012
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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)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
7
2523-5141
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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.
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
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nam a22 5a 4500
10.4171/021
DE-4084
2006-04-30
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10.4171/021
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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)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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nam a22 5a 4500
10.4171/013
DE-4084
2005-05-31
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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)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
8
2523-5141
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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
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nam a22 5a 4500
10.4171/011
DE-4084
2006-01-10
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10.4171/011
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Hjorth
edt
Dynamics on the Riemann Sphere ;
A Bodil Branner Festschrift.
EMS Press
2006
1 online resource (226 pages)
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_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).
Mathematics
bicssc
Lunde Petersen
edt
https://ems.press/doi/10.4171/011
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nam a22 5a 4500
10.4171/014
DE-4084
2005-08-30
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9783037195147
10.4171/014
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DE-4084
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bicssc
Trzeciak
aut
Writing Mathematical Papers in English ;
a practical guide.
EMS Press
2005
1 online resource (51 pages)
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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 [www.impan.gov.pl/Dictionary](http://www.impan.gov.pl/Dictionary).
Mathematics
bicssc
https://ems.press/doi/10.4171/014
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nam a22 5a 4500
10.4171/015
DE-4084
2006-02-14
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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)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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nam a22 5a 4500
10.4171/017
DE-4084
2006-02-28
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9783037195178
10.4171/017
doi
DE-4084
PBKJ
bicssc
34A09
msc
65L80
msc
Kunkel
aut
Differential-Algebraic Equations ;
Analysis and Numerical Solution.
EMS Press
2006
1 online resource (385 pages)
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EMS Textbooks in Mathematics (etb)
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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.
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
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nam a22 5a 4500
10.4171/016
DE-4084
2006-02-28
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9783037195161
10.4171/016
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DE-4084
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)
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EMS Textbooks in Mathematics (etb)
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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.
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
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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)
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**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
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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)
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**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
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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
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rdamedia
online resource
cr
rdacarrier
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PDF
rda
Restricted to subscribers.
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**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
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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
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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)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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nam a22 5a 4500
10.4171/024
DE-4084
2006-06-30
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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)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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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)
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ESI Lectures in Mathematics and Physics (esi)
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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
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nam a22 5a 4500
10.4171/027
DE-4084
2007-01-10
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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)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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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
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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nam a22 5a 4500
10.4171/028
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2006-10-12
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68R15
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Nyssen
edt
Physics and Number Theory.
EMS Press
2006
1 online resource (274 pages)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
10
2523-5141
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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.
Mathematics
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
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nam a22 5a 4500
10.4171/020
DE-4084
2006-12-01
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10.4171/020
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70H05
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14H10
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17B37
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17B40
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17B67
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32S40
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35C20
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53D30
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70G65
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82B23
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Bertrand
edt
Differential Equations and Quantum Groups ;
Andrey A. Bolibrukh Memorial Volume.
EMS Press
2006
1 online resource (302 pages)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
9
2523-5141
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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
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2007-01-10
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10.4171/031
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Christodoulou
aut
The Formation of Shocks in 3-Dimensional Fluids.
EMS Press
2007
1 online resource (1000 pages)
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EMS Monographs in Mathematics (emm)
2523-5206
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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
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nam a22 5a 4500
10.4171/034
DE-4084
2007-03-03
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PBMS
bicssc
16G30
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70H06
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16S80
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14A22
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Etingof
aut
Calogero-Moser systems and representation theory.
EMS Press
2007
1 online resource (101 pages)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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nam a22 5a 4500
10.4171/038
DE-4084
2007-04-04
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12-XX
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Iwaniec
edt
Andrzej Schinzel, Selecta.
EMS Press
2007
1 online resource (1417 pages)
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Heritage of European Mathematics (hem)
2523-5222
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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
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nam a22 5a 4500
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msc
12-XX
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Iwaniec
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Andrzej Schinzel, Selecta.
Volume I. Diophantine Problems and Polynomials
EMS Press
2007
1 online resource (1417 pages)
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rdacarrier
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Heritage of European Mathematics (hem)
2523-5222
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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
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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)
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rdacarrier
text file
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Heritage of European Mathematics (hem)
2523-5222
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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
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070321e20070321gw fot 00| 0|eng d
9783037195376
10.4171/037
doi
DE-4084
PBMP
bicssc
PBKJ
bicssc
58J45
msc
81T20
msc
35L05
msc
35L15
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53C50
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81T05
msc
Bär
aut
Wave Equations on Lorentzian Manifolds and Quantization.
EMS Press
2007
1 online resource (202 pages)
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ESI Lectures in Mathematics and Physics (esi)
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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
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nam a22 5a 4500
10.4171/029
DE-4084
2007-05-25
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PBKD
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30-00
msc
32G15
msc
30F60
msc
30C62
msc
57N16
msc
53A35
msc
20F65
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30F20
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30F25
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30F10
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30F30
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30F40
msc
30F45
msc
14H15
msc
20H10
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30F15
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53B35
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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)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
11
2523-5141
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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
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10.4171/033
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2007-05-31
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35K65
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Daskalopoulos
aut
Degenerate Diffusions ;
Initial Value Problems and Local Regularity Theory.
EMS Press
2007
1 online resource (207 pages)
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EMS Tracts in Mathematics (etm)
1
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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
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10.4171/032
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2007-05-31
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10.4171/032
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DE-4084
PBP
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22-02
msc
17B65
msc
22D05
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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)
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EMS Tracts in Mathematics (etm)
2
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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
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nam a22 5a 4500
10.4171/036
DE-4084
2007-05-24
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9783037195369
10.4171/036
doi
DE-4084
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51F99
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53C23
msc
55M10
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54C20
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20F67
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20F69
msc
Buyalo
aut
Elements of Asymptotic Geometry.
EMS Press
2007
1 online resource (212 pages)
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EMS Monographs in Mathematics (emm)
2523-5206
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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
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nam a22 5a 4500
10.4171/039
DE-4084
2007-08-06
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9783037195390
10.4171/039
doi
DE-4084
PBMW
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19-02
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46-02
msc
46L80
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46A17
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46H30
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19D55
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19K35
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Meyer
aut
Local and Analytic Cyclic Homology.
EMS Press
2007
1 online resource (368 pages)
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EMS Tracts in Mathematics (etm)
3
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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.
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
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nam a22 5a 4500
10.4171/035
DE-4084
2007-09-06
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070906e20070906gw fot 00| 0|eng d
9783037195352
10.4171/035
doi
DE-4084
PBT
bicssc
60G70
msc
60F99
msc
91B70
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62G32
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60G55
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Balkema
aut
High Risk Scenarios and Extremes ;
A geometric approach.
EMS Press
2007
1 online resource (389 pages)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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071121e20071121gw fot 00| 0|eng d
9783037195406
10.4171/040
doi
DE-4084
PBKJ
bicssc
35-02
msc
35J25
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35S15
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Harutyunyan
aut
Elliptic Mixed, Transmission and Singular Crack Problems.
EMS Press
2007
1 online resource (777 pages)
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EMS Tracts in Mathematics (etm)
4
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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
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071121e20071121gw fot 00| 0|eng d
9783037195420
10.4171/042
doi
DE-4084
PBKJ
bicssc
35-01
msc
46-01
msc
35J25
msc
35P15
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42B35
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46E35
msc
46F05
msc
47B06
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47F05
msc
Haroske
aut
Distributions, Sobolev Spaces, Elliptic Equations.
EMS Press
2007
1 online resource (303 pages)
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EMS Textbooks in Mathematics (etb)
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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
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nam a22 5a 4500
10.4171/044
DE-4084
2008-02-12
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080212e20080212gw fot 00| 0|eng d
9783037195444
10.4171/044
doi
DE-4084
PBKQ
bicssc
28A75
msc
26B15
msc
49Q15
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49Q20
msc
De Lellis
aut
Rectifiable Sets, Densities, and Tangent Measures.
EMS Press
2008
1 online resource (133 pages)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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nam a22 5a 4500
10.4171/043
DE-4084
2008-02-28
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080228e20080228gw fot 00| 0|eng d
9783037195437
10.4171/043
doi
DE-4084
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)
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EMS Textbooks in Mathematics (etb)
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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.
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
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nam a22 5a 4500
10.4171/041
DE-4084
2008-02-29
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080229e20080229gw fot 00| 0|eng d
9783037195413
10.4171/041
doi
DE-4084
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)
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EMS Textbooks in Mathematics (etb)
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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.
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
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nam a22 5a 4500
10.4171/049
DE-4084
2008-03-03
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080303e20080303gw fot 00| 0|eng d
9783037195499
10.4171/049
doi
DE-4084
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)
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EMS Textbooks in Mathematics (etb)
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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.
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
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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)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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nam a22 5a 4500
10.4171/045
DE-4084
2008-04-29
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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)
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EMS Tracts in Mathematics (etm)
5
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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
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nam a22 5a 4500
10.4171/054
DE-4084
2008-08-19
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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)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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10.4171/052
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2008-09-01
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05A15
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52B45
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52B55
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52C45
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11H06
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Barvinok
aut
Integer Points in Polyhedra.
EMS Press
2008
1 online resource (199 pages)
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Zurich Lectures in Advanced Mathematics (zlam)
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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.
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
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nam a22 5a 4500
10.4171/047
DE-4084
2008-06-11
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bicssc
81R50
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81R12
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Enriquez
edt
Quantum Groups.
EMS Press
2008
1 online resource (140 pages)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
12
2523-5141
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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.
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
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nam a22 5a 4500
10.4171/051
DE-4084
2008-06-11
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DE-4084
PBMP
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53C50
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Alekseevsky
edt
Recent Developments in Pseudo-Riemannian Geometry.
EMS Press
2008
1 online resource (549 pages)
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ESI Lectures in Mathematics and Physics (esi)
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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
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nam a22 5a 4500
10.4171/018
DE-4084
2008-06-26
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10.4171/018
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42C40
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65T60
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Mohlenkamp
aut
Wavelets, Their Friends, and What They Can Do for You.
EMS Press
2008
1 online resource (119 pages)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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
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nam a22 5a 4500
10.4171/065
DE-4084
2008-07-04
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Schmitt
aut
Geometric Invariant Theory and Decorated Principal Bundles.
EMS Press
2008
1 online resource (396 pages)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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nam a22 5a 4500
10.4171/019
DE-4084
2008-09-02
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10.4171/019
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DE-4084
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46-02
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46E35
msc
42C40
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42B35
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28A80
msc
Triebel
aut
Function Spaces and Wavelets on Domains.
EMS Press
2008
1 online resource (265 pages)
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EMS Tracts in Mathematics (etm)
7
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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.
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
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nam a22 5a 4500
10.4171/026
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2008-09-02
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65Y20
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68Q17
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68Q25
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41A63
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46E22
msc
28C20
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46E30
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Novak
aut
Tractability of Multivariate Problems.
Volume I. Linear Information
EMS Press
2008
1 online resource (395 pages)
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EMS Tracts in Mathematics (etm)
6
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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.
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
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nam a22 5a 4500
10.4171/048
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2008-09-01
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tom Dieck
aut
Algebraic Topology ;
Corrected 2nd printing, 2010.
EMS Press
2008
1 online resource (578 pages)
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EMS Textbooks in Mathematics (etb)
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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
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nam a22 5a 4500
10.4171/067
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2008-09-24
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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)
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Zurich Lectures in Advanced Mathematics (zlam)
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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.
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
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nam a22 5a 4500
10.4171/062
DE-4084
2008-09-24
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32Sxx
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55Pxx
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57Mxx
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81Rxx
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Skowroński
edt
Trends in Representation Theory of Algebras and Related Topics.
EMS Press
2008
1 online resource (722 pages)
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EMS Series of Congress Reports (ecr)
2523-5168
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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.
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
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2008-10-06
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Cortiñas
edt
K-Theory and Noncommutative Geometry.
EMS Press
2008
1 online resource (454 pages)
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EMS Series of Congress Reports (ecr)
2523-5168
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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
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2008-10-22
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DE-4084
PB
bicssc
01-02
msc
82-02
msc
82C03
msc
82B40
msc
Gallavotti
edt
Boltzmanns Legacy.
EMS Press
2008
1 online resource (284 pages)
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ESI Lectures in Mathematics and Physics (esi)
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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.
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
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10.4171/068
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2009-01-10
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10.4171/068
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35L70
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35Q75
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58J45
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83C75
msc
Christodoulou
aut
The Formation of Black Holes in General Relativity.
EMS Press
2009
1 online resource (599 pages)
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EMS Monographs in Mathematics (emm)
2523-5206
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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.
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
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nam a22 5a 4500
10.4171/059
DE-4084
2008-12-01
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9783037195598
10.4171/059
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DE-4084
PBX
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01-02
msc
Beery
edt
Thomas Harriots Doctrine of Triangular Numbers: the Magisteria Magna.
EMS Press
2008
1 online resource (144 pages)
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Heritage of European Mathematics (hem)
2523-5222
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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
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nam a22 5a 4500
10.4171/055
DE-4084
2009-03-25
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9783037195550
10.4171/055
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DE-4084
PBKD
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msc
32-00
msc
32G15
msc
30F60
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14A20
msc
14C17
msc
14D20
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14H15
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14H60
msc
14L24
msc
14L35
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16R30
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20F36
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20F38
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20F65
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22F10
msc
20H10
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30F10
msc
30F15
msc
30F20
msc
30F25
msc
30C62
msc
51N15
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53A20
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53A35
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53B35
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53C24
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53C25
msc
53C50
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57M07
msc
57M60
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57R20
msc
Papadopoulos
edt
Handbook of Teichmüller Theory, Volume II.
EMS Press
2009
1 online resource (883 pages)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
13
2523-5141
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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
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10.4171/066
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2009-04-08
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05B05
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51E05
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51E12
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51E14
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51E20
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51E21
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51E30
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Payne
aut
Finite Generalized Quadrangles ;
Second Edition.
EMS Press
2009
1 online resource (299 pages)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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nam a22 5a 4500
10.4171/056
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2009-06-15
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9783037195567
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DE-4084
PBKJ
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00Bxx
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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)
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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
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nam a22 5a 4500
10.4171/053
DE-4084
2009-06-08
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9783037195536
10.4171/053
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DE-4084
PBKJ
bicssc
83-02
msc
83C75
msc
Ringström
aut
The Cauchy Problem in General Relativity.
EMS Press
2009
1 online resource (307 pages)
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ESI Lectures in Mathematics and Physics (esi)
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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.
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
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nam a22 5a 4500
10.4171/070
DE-4084
2009-07-08
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9783037195703
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DE-4084
PHDD
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PB
bicssc
82-02
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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)
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EMS Tracts in Mathematics (etm)
8
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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.
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
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nam a22 5a 4500
10.4171/069
DE-4084
2009-06-24
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9783037195697
10.4171/069
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DE-4084
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)
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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.
Mathematics
bicssc
Numerical analysis
msc
History and biography
msc
Sloan
aut
Traub
aut
Woźniakowski
aut
https://ems.press/doi/10.4171/069
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nam a22 5a 4500
10.4171/064
DE-4084
2009-08-08
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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)
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EMS Textbooks in Mathematics (etb)
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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
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nam a22 5a 4500
10.4171/071
DE-4084
2009-08-15
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10.4171/071
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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)
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EMS Textbooks in Mathematics (etb)
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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
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nam a22 5a 4500
10.4171/046
DE-4084
2009-08-29
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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)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
14
2523-5141
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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, Birkhoff's pointwise theorem, dominated ergodic theorems, oscillations functions of ergodic averages, transference principle, Wiener-Wintner theorem, Banach principle, continuity principle, Bourgain's 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(nkx), k 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
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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
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2009-09-24
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34M30
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34M35
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81T15
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81T18
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81T75
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11S40
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33B30
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34M50
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Connes
edt
Renormalization and Galois Theories.
EMS Press
2009
1 online resource (279 pages)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
15
2523-5141
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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
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
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nam a22 5a 4500
10.4171/074
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2009-10-01
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Böckle
aut
Cohomological Theory of Crystals over Function Fields.
EMS Press
2009
1 online resource (195 pages)
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EMS Tracts in Mathematics (etm)
9
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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.
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
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nam a22 5a 4500
10.4171/058
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2009-10-30
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Springer
edt
Hans Freudenthal, Selecta.
EMS Press
2009
1 online resource (661 pages)
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Heritage of European Mathematics (hem)
2523-5222
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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
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nam a22 5a 4500
10.4171/128
DE-4084
2013-12-13
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Khalkhali
aut
Basic Noncommutative Geometry ;
Second edition.
EMS Press
2013
1 online resource (257 pages)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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.
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
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nam a22 5a 4500
10.4171/076
DE-4084
2010-02-26
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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)
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ESI Lectures in Mathematics and Physics (esi)
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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
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nam a22 5a 4500
10.4171/077
DE-4084
2010-04-24
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00Bxx
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Ran
edt
European Congress of Mathematics ;
Amsterdam, 14-18 July, 2008.
EMS Press
2010
1 online resource (488 pages)
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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
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nam a22 5a 4500
10.4171/078
DE-4084
2010-04-30
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9783037195789
10.4171/078
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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)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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nam a22 5a 4500
10.4171/081
DE-4084
2010-05-19
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10.4171/081
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DE-4084
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)
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EMS Textbooks in Mathematics (etb)
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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.
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
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nam a22 5a 4500
10.4171/086
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2010-06-01
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DE-4084
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msc
81-02
msc
16-02
msc
18-02
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Turaev
aut
Homotopy Quantum Field Theory ;
With Appendices by Michael Müger and Alexis Virelizier.
EMS Press
2010
1 online resource (290 pages)
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EMS Tracts in Mathematics (etm)
10
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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.
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
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nam a22 5a 4500
10.4171/085
DE-4084
2010-06-01
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9783037195857
10.4171/085
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DE-4084
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)
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EMS Tracts in Mathematics (etm)
11
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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).
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
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nam a22 5a 4500
10.4171/079
DE-4084
2010-06-10
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9783037195796
10.4171/079
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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)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
16
2523-5141
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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
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nam a22 5a 4500
10.4171/084
DE-4084
2010-07-03
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10.4171/084
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46E30
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11K38
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Novak
aut
Tractability of Multivariate Problems.
Volume II. Standard Information for Functionals
EMS Press
2010
1 online resource (675 pages)
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EMS Tracts in Mathematics (etm)
12
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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.
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
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nam a22 5a 4500
10.4171/093
DE-4084
2010-09-07
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10.4171/093
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68Qxx
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90Bxx
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90Cxx
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Onn
aut
Nonlinear Discrete Optimization ;
An Algorithmic Theory.
EMS Press
2010
1 online resource (147 pages)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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nam a22 5a 4500
10.4171/089
DE-4084
2010-08-24
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9783037195895
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Colbois
edt
math.ch/100 ;
Schweizerische Mathematische Gesellschaft - Société Mathématique Suisse - Swiss Mathematical Society 1910.
EMS Press
2010
1 online resource (526 pages)
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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
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nam a22 5a 4500
10.4171/090
DE-4084
2010-09-29
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10.4171/090
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Harada
aut
Moonshine of Finite Groups.
EMS Press
2010
1 online resource (83 pages)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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.
Mathematics
bicssc
General theory for finite permutation groups
msc
Modular and automorphic functions
msc
https://ems.press/doi/10.4171/090
cover image
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nam a22 5a 4500
10.4171/082
DE-4084
2010-09-29
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9783037195826
10.4171/082
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DE-4084
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57M50
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Bessières
aut
Geometrisation of 3-Manifolds.
EMS Press
2010
1 online resource (247 pages)
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EMS Tracts in Mathematics (etm)
13
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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.
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
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nam a22 5a 4500
10.4171/087
DE-4084
2010-12-01
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10.4171/087
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53-01
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53-03
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53A35
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Papadopoulos
edt
Nikolai I. Lobachevsky, Pangeometry.
EMS Press
2010
1 online resource (322 pages)
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Heritage of European Mathematics (hem)
2523-5222
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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.
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
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nam a22 5a 4500
10.4171/007
DE-4084
2010-12-30
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14E30
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Faber
edt
Classification of Algebraic Varieties.
EMS Press
2010
1 online resource (346 pages)
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EMS Series of Congress Reports (ecr)
2523-5168
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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
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nam a22 5a 4500
10.4171/091
DE-4084
2010-12-01
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9783037195918
10.4171/091
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DE-4084
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65-02
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65F05
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65N22
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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)
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EMS Tracts in Mathematics (etm)
14
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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.
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
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nam a22 5a 4500
10.4171/080
DE-4084
2011-02-25
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47G10
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32M15
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14K25
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47B50
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Neretin
aut
Lectures on Gaussian Integral Operators and Classical Groups.
EMS Press
2011
1 online resource (571 pages)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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nam a22 5a 4500
10.4171/092
DE-4084
2011-03-29
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DE-4084
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01A40
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01A45
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01A50
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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)
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Heritage of European Mathematics (hem)
2523-5222
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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
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nam a22 5a 4500
10.4171/096
DE-4084
2011-06-11
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17B56
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14F43
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Calaque
aut
Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry.
EMS Press
2011
1 online resource (114 pages)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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nam a22 5a 4500
10.4171/008
DE-4084
2011-07-06
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11G09
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11M06
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11M32
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47G30
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81Q30
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81T15
msc
17A30
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16T30
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46L80
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46L87
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19K33
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19K56
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58J42
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Carey
edt
Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory.
EMS Press
2011
1 online resource (280 pages)
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ESI Lectures in Mathematics and Physics (esi)
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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
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nam a22 5a 4500
10.4171/083
DE-4084
2011-08-11
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55U35
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57M05
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57M10
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57M15
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Brown
aut
Nonabelian Algebraic Topology ;
Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids.
EMS Press
2011
1 online resource (703 pages)
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EMS Tracts in Mathematics (etm)
15
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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
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nam a22 5a 4500
10.4171/098
DE-4084
2011-08-11
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10.4171/098
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Jarnicki
aut
Separately Analytic Functions.
EMS Press
2011
1 online resource (306 pages)
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EMS Tracts in Mathematics (etm)
16
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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
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nam a22 5a 4500
10.4171/097
DE-4084
2011-08-06
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10.4171/097
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58A50
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58C50
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14M30
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17A70
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32C11
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81Q60
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Carmeli
aut
Mathematical Foundations of Supersymmetry.
EMS Press
2011
1 online resource (300 pages)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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nam a22 5a 4500
10.4171/072
DE-4084
2011-08-10
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9783037195727
10.4171/072
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DE-4084
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bicssc
60-06
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60Gxx
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60Jxx
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Blath
edt
Surveys in Stochastic Processes.
EMS Press
2011
1 online resource (263 pages)
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EMS Series of Congress Reports (ecr)
2523-5168
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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
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nam a22 5a 4500
10.4171/095
DE-4084
2011-09-02
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37D10
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Nakanishi
aut
Invariant Manifolds and Dispersive Hamiltonian Evolution Equations.
EMS Press
2011
1 online resource (258 pages)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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nam a22 5a 4500
10.4171/101
DE-4084
2011-09-24
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9783037196014
10.4171/101
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Skowroński
edt
Representations of Algebras and Related Topics.
EMS Press
2011
1 online resource (740 pages)
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EMS Series of Congress Reports (ecr)
2523-5168
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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
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nam a22 5a 4500
10.4171/088
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2011-09-25
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Girard
aut
The Blind Spot ;
Lectures on Logic.
EMS Press
2011
1 online resource (550 pages)
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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
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nam a22 5a 4500
10.4171/104
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2011-10-20
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20-03
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20D05
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33-03
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33E05
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Neumann
aut
The mathematical writings of Évariste Galois ;
Corrected 2nd printing, September 2013.
EMS Press
2011
1 online resource (421 pages)
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Heritage of European Mathematics (hem)
2523-5222
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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
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10.4171/099
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2011-11-05
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49J52
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49N60
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49Q20
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58C99
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58J05
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58J32
msc
Björn
aut
Nonlinear Potential Theory on Metric Spaces.
EMS Press
2011
1 online resource (415 pages)
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EMS Tracts in Mathematics (etm)
17
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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
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16G70
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Skowroński
aut
Frobenius Algebras I ;
Basic Representation Theory.
EMS Press
2011
1 online resource (661 pages)
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EMS Textbooks in Mathematics (etb)
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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
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10.4171/100
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65P10
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37M15
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35Q41
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Faou
aut
Geometric Numerical Integration and Schrödinger Equations.
EMS Press
2012
1 online resource (146 pages)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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nam a22 5a 4500
10.4171/075
DE-4084
2012-01-02
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9783037195758
10.4171/075
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PBKD
bicssc
30-02
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30F60
msc
32G15
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30F10
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30Fxx
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Penner
aut
Decorated Teichmüller Theory.
EMS Press
2012
1 online resource (377 pages)
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The QGM Master Class Series (qgm)
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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
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nam a22 5a 4500
10.4171/105
DE-4084
2012-01-18
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9783037196052
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37E30
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51E24
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53C23
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53C35
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53C70
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54C20
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57M15
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57M50
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Papadopoulos
edt
Strasbourg Master Class on Geometry.
EMS Press
2012
1 online resource (461 pages)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
18
2523-5141
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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
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2012-02-09
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PBMP
bicssc
35L05
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35L52
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Krieger
aut
Concentration Compactness for Critical Wave Maps.
EMS Press
2012
1 online resource (490 pages)
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EMS Monographs in Mathematics (emm)
2523-5206
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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
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Triebel
aut
Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration.
EMS Press
2012
1 online resource (115 pages)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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PBF
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17B10
msc
17B55
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Mazorchuk
aut
Lectures on Algebraic Categorification.
EMS Press
2012
1 online resource (128 pages)
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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
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2012-05-11
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PBT
bicssc
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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)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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nam a22 5a 4500
10.4171/110
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2012-06-13
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9783037196106
10.4171/110
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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)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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nam a22 5a 4500
10.4171/103
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2012-06-08
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msc
57-00
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msc
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11F75
msc
14D20
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msc
14H60
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30F10
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30F15
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msc
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msc
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msc
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53B35
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53C35
msc
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msc
53C80
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53D55
msc
53Z05
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57M07
msc
57M50
msc
57M60
msc
57N16
msc
Papadopoulos
edt
Handbook of Teichmüller Theory, Volume III.
EMS Press
2012
1 online resource (874 pages)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
17
2523-5141
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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
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13D10
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14-02
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14B05
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14B12
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14C17
msc
14C20
msc
14C35
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14D06
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14D15
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14D20
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14D23
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14E15
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14E30
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14F43
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14J28
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14J30
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14J50
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14L30
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14M17
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14M25
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14N15
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32Q45
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34A30
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53D05
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55N91
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01-02
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01A70
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05E05
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11S85
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13A35
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14C30
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14N20
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Pragacz
edt
Contributions to Algebraic Geometry ;
Impanga Lecture Notes.
EMS Press
2012
1 online resource (516 pages)
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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
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de Jong
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Geometry and Arithmetic.
EMS Press
2012
1 online resource (383 pages)
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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
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10.4171/112
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Nowak
aut
Large Scale Geometry.
EMS Press
2012
1 online resource (203 pages)
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EMS Textbooks in Mathematics (etb)
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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
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10.4171/116
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Novak
aut
Tractability of Multivariate Problems.
Volume III. Standard Information for Operators
EMS Press
2012
1 online resource (604 pages)
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EMS Tracts in Mathematics (etm)
18
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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
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18F30
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32A27
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32C37
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32G15
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35Q75
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52C35
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53C05
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55N35
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55R40
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57R18
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57R20
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58A30
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58K40
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58K60
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60D05
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83C57
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Blanlil
edt
Singularities in Geometry and Topology ;
Strasbourg 2009.
EMS Press
2012
1 online resource (370 pages)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
20
2523-5141
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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
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10.4171/115
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16E05
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16E40
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18G10
msc
20G05
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20G15
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Kawamata
edt
Derived Categories in Algebraic Geometry ;
Tokyo 2011.
EMS Press
2013
1 online resource (354 pages)
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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
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11E04
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11E88
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11R18
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11R37
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11U10
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Roquette
aut
Contributions to the History of Number Theory in the 20th Century.
EMS Press
2013
1 online resource (289 pages)
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Heritage of European Mathematics (hem)
2523-5222
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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
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10.4171/121
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81-03
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81P15
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Reiter
edt
Erwin Schrödinger - 50 Years After.
EMS Press
2013
1 online resource (195 pages)
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ESI Lectures in Mathematics and Physics (esi)
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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
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nam a22 5a 4500
10.4171/111
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31-01
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Bruna
aut
Complex Analysis ;
Translated from the Catalan by Ignacio Monreal.
EMS Press
2013
1 online resource (576 pages)
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EMS Textbooks in Mathematics (etb)
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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
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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)
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EMS Tracts in Mathematics (etm)
19
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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.png
nam a22 5a 4500
10.4171/123
DE-4084
2013-05-29
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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)
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EMS Tracts in Mathematics (etm)
20
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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
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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)
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EMS Tracts in Mathematics (etm)
21
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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.png
nam a22 5a 4500
10.4171/126
DE-4084
2013-11-15
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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
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Heritage of European Mathematics (hem)
2523-5222
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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
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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
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rdacontent
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rdacarrier
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rda
Heritage of European Mathematics (hem)
2523-5222
Restricted to subscribers.
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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
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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)
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
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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)
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
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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)
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
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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)
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Zurich Lectures in Advanced Mathematics (zlam)
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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.png
nam a22 5a 4500
10.4171/120
DE-4084
2014-01-03
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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)
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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
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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)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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2014-01-18
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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)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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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)
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EMS Series of Congress Reports (ecr)
2523-5168
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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
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nam a22 5a 4500
10.4171/131
DE-4084
2014-03-15
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9783037196311
10.4171/131
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DE-4084
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35Q55
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37K15
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37K10
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34L40
msc
34L20
msc
Grébert
aut
The Defocusing NLS Equation and Its Normal Form.
EMS Press
2014
1 online resource (175 pages)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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
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nam a22 5a 4500
10.4171/138
DE-4084
2014-05-10
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9783037196380
10.4171/138
doi
DE-4084
PBM
bicssc
51-01
msc
51N15
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51N10
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51N20
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Casas-Alvero
aut
Analytic Projective Geometry.
EMS Press
2014
1 online resource (636 pages)
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EMS Textbooks in Mathematics (etb)
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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
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nam a22 5a 4500
10.4171/137
DE-4084
2014-04-28
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9783037196373
10.4171/137
doi
DE-4084
PB
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PBC
bicssc
00-02
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01-02
msc
Deuflhard
edt
MATHEON - Mathematics for Key Technologies.
EMS Press
2014
1 online resource (466 pages)
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EMS Series in Industrial and Applied Mathematics (esiam)
1
2523-5095
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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.png
nam a22 5a 4500
10.4171/117
DE-4084
2014-05-30
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9783037196175
10.4171/117
doi
DE-4084
PBKD
bicssc
30-00
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32-00
msc
57-00
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32G13
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32G15
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30F60
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11F06
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11F75
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14D20
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14H15
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14H60
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14H55
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14J60
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20F14
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20F28
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20F38
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20F65
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20F67
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20H10
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22E46
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30-03
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30C62
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30F20
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30F25
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30F10
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30F15
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30F30
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30F35
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30F40
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30F45
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32-03
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32S30
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53A35
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53B35
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53C35
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53C50
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53C80
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53D55
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53Z05
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57M07
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57M50
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57M60
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57N16
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Papadopoulos
edt
Handbook of Teichmüller Theory, Volume IV.
EMS Press
2014
1 online resource (838 pages)
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IRMA Lectures in Mathematics and Theoretical Physics (irma)
19
2523-5141
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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
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9783037196342
10.4171/134
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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)
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Zurich Lectures in Advanced Mathematics (zlam)
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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
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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)
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EMS Textbooks in Mathematics (etb)
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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
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140901e20140901gw fot 00| 0|eng d
9783037196496
10.4171/149
doi
DE-4084
PB
bicssc
12E30
msc
12F10
msc
13A18
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14H20
msc
14M25
msc
11U09
msc
12E05
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12F05
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12L12
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13D40
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13F30
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13H05
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13N15
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14C20
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14F10
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14J17
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16W60
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32P05
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37A05
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54F50
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Campillo
edt
Valuation Theory in Interaction.
EMS Press
2014
1 online resource (670 pages)
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EMS Series of Congress Reports (ecr)
2523-5168
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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
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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)
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EMS Series of Lectures in Mathematics (elm)
2523-5184
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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 univ