New Book Releases - Spring/Summer 2020

2020 has been a busy year for our books programme, with a number of new titles published during the spring/summer period. Spanning a range of disciplines, new titles from this period include:

• Handbook of Teichmüller Theory, Volume VII

• Algebraic Combinatorics, Resurgence, Moulds and Applications Vol. 1 & Vol. 2

• K3 Surfaces

• t-Motives: Hodge Structures, Transcendence, and Other Motivic Aspects

• Decision Support Systems for Water Supply Systems

• Classification of Complex Algebraic Surfaces

Read on to find out more about each title.

Handbook of Teichmüller Theory, Volume VII (published February 2020)

Series: IRMA Lectures in Mathematics and Theoretical Physics

Editor: Athanase Papadopoulos (Université de Strasbourg, France)

The present volume of the Handbook of Teichmüller theory is divided into three parts.

The first part contains surveys on various topics in Teichmüller theory, including the complex structure of Teichmüller space, the Deligne–Mumford compactification of the moduli space, holomorphic quadratic differentials, Kleinian groups, hyperbolic 3-manifolds and the ending lamination theorem, the universal Teichmüller space, barycentric extensions of maps of the circle, and the theory of Higgs bundles.

The second part consists of three historico-geometrical articles on Tissot (a precursor of the theory of quasiconfomal mappings), Grötzsch and Lavrentieff, the two main founders of the modern theory of quasiconformal mappings.

The third part comprises English translations of five papers by Grötzsch, a paper by Lavrentieff, and three papers by Teichmüller. These nine papers are foundational essays on the theories of conformal invariants and quasiconformal mappings, with applications to conformal geometry, to the type problem and to Nevanlinna's theory. The papers are followed by commentaries that highlight the relations between them and between later works on the subject. These papers are not only historical documents; they constitute an invaluable source of ideas for current research in Teichmüller theory.

Algebraic Combinatorics, Resurgence, Moulds and Applications, Volume 1 & Volume 2 (published February 2020)

Series: IRMA Lectures in Mathematics and Theoretical Physics

Editors: Frédéric Chapoton (Université de Strasbourg, France) Frédéric Fauvet (Université de Strasbourg, France) Claudia Malvenuto (Università di Roma La Sapienza, Italy) Jean-Yves Thibon (Université Paris-Est Marne-la-Vallée, France)

A 2-volume work comprising a total of 14 refereed research articles which stem from the CARMA Conference (Algebraic Combinatorics, Resurgence, Moulds and Applications), held at the Centre International de Rencontres Mathématiques in Luminy, France, from June 26 to 30, 2017.

The conference did notably emphasise the role of Hopf algebraic techniques and related concepts (e.g. Rota–Baxter algebras, operads, Ecalle’s mould calculus) which have lately proved pervasive in combinatorics, but also in many other fields, from multiple zeta values to the algebraic study of control systems and the theory of rough paths.

The volumes should be useful to researchers or graduate students in mathematics working in these domains and to theoretical physicists involved with resurgent functions and alien calculus.

K3 Surfaces (published March 2020)

Series: EMS Tracts in Mathematics

Shigeyuki Kondō (Nagoya University, Japan)

K3 surfaces are a key piece in the classification of complex analytic or algebraic surfaces. The term was coined by A. Weil in 1958 – a result of the initials Kummer, Kähler, Kodaira, and the mountain K2 found in Karakoram. The most famous example is the Kummer surface discovered in the 19th century.

K3 surfaces can be considered as a 2-dimensional analogue of an elliptic curve, and the theory of periods – called the Torelli-type theorem for K3 surfaces – was established around 1970. Since then, several pieces of research on K3 surfaces have been undertaken and more recently K3 surfaces have even become of interest in theoretical physics.

The main purpose of this book is an introduction to the Torelli-type theorem for complex analytic K3 surfaces, and its applications. The theory of lattices and their reflection groups is necessary to study K3 surfaces, and this book introduces these notions. The book contains, as well as lattices and reflection groups, the classification of complex analytic surfaces, the Torelli-type theorem, the subjectivity of the period map, Enriques surfaces, an application to the moduli space of plane quartics, finite automorphisms of K3 surfaces, Niemeier lattices and the Mathieu group, the automorphism group of Kummer surfaces and the Leech lattice.

The author seeks to demonstrate the interplay between several sorts of mathematics and hopes the book will prove helpful to researchers in algebraic geometry and related areas, and to graduate students with a basic grounding in algebraic geometry.

t-Motives: Hodge Structures, Transcendence and Other Motivic Aspects (published May 2020)

Series: EMS Series of Congress Reports

Editors: Gebhard Böckle (Universität Heidelberg, Germany) David Goss Urs Hartl (Universität Münster, Germany) Matthew A. Papanikolas (Texas A&M University, College Station, USA)

This volume contains research and survey articles on Drinfeld modules, Anderson t-modules and t-motives. Much material that had not been easily accessible in the literature is presented here, for example the cohomology theories and Pink’s theory of Hodge structures attached to Drinfeld modules and t-motives. Also included are survey articles on the function field analogue of Fontaine’s theory of p-adic crystalline Galois representations and on transcendence methods over function fields, encompassing the theories of Frobenius difference equations, automata theory, and Mahler’s method. In addition, this volume contains a small number of research articles on function field Iwasawa theory, 1-t-motifs, and multizeta values.

This book is a useful source for learning important techniques and an effective reference for all researchers working in or interested in the area of function field arithmetic, from graduate students to established experts.

Decision Support Systems for Water Supply Systems (published May 2020)

Series: EMS Series in Industrial and Applied Mathematics

Editors: Andreas Pirsing (Siemens AG, Berlin, Germany) Antonio Morsi (Universität Erlangen-Nürnberg, Germany)

Operating water supply systems is complex. Engineers must ensure that consumers are reliably supplied with a sufficient quantity and quality of water, as well as a sufficient water pressure at all times – all while maintaining reasonable prices. This book summarizes the results of the German BMBF (Federal Ministry of Education and Research) funded joint research project, EWave (Project ID: 02WER1323F), that was initiated to develop an innovative Decision Support System (DSS) for water supply companies. For decision making and operational support, the EWave system uses newly developed integrated optimization modules. As a result, the user receives operating schedules on a 15 minute scale. To achieve this, mixed-integer linear and nonlinear mathematical optimization methods are combined. First, a mixed-integer optimization model is solved in order to derive all discrete decisions (primarily pump schedules). The aim is to approximate the physics by piecewise linear relaxations sufficiently to optimize decisions. EWave then uses nonlinear optimization and simulation methods to verify the physics. The process is iterated as necessary. This approach enables globally optimal solutions within an a priori given quality tolerance.

Optimization results obtained in real time yield a potential of energy savings of up to 4–6% daily for the waterworks in the pilot area.

This book was written for automation experts in water supply companies as well as mathematicians who work for infrastructure companies.

Classification of Complex Algebraic Surfaces (published June 2020)

Series: EMS Series of Lectures in Mathematics

Ciro Ciliberto (Università di Roma Tor Vergata, Italy)

Τhe classification of complex algebraic surfaces is a very classical subject which goes back to the old Italian school of algebraic geometry with Enriques and Castelnuovo. However, the exposition in the present book is modern and follows Mori's approach to the classification of algebraic varieties. The text includes the P12 theorem, the Sarkisov programme in the surface case and the Noether–Castelnuovo theorem in its classical version.

This book serves as a relatively quick and handy introduction to the theory of algebraic surfaces and is intended for readers with a good knowledge of basic algebraic geometry. Although an acquaintance with the basic parts of books like Principles of Algebraic Geometry by Griffiths and Harris or Algebraic Geometry by Hartshorne should be sufficient, the author strove to make the text as self-contained as possible and, for this reason, a first chapter is devoted to a quick exposition of some preliminaries.