2014-12-94

New books published by theIndividual members of the EMS, membersocieties or societies with a reciprocity agreement(such as the American, Australian andCanadian Mathematical Societies) are entitledto a discount of 20% on any book purchases, ifordered directly at the EMS Publishing House.Hans Triebel (University of Jena, Germany)Hybrid Function Spaces, Heat and Navier–Stokes Equations (Tracts in Mathematics Vol. 24)ISBN 978-3-03719-150-7. 2015. 196 pages. Hardcover. 17 x 24 cm. 48.00 EuroThis book is the continuation of Local Function Spaces, Heat and Navier–Stokes Equations (Tracts in Mathematics 20, 2013) by theauthor. A new approach is presented to exhibit relations between Sobolev spaces, Besov spaces, and Hölder–Zygmund spaces on theone hand and Morrey–Campanato spaces on the other. Morrey–Campanato spaces extend the notion of functions of bounded meanoscillation. These spaces play a crucial role in the theory of linear and nonlinear PDEs.Chapter 1 (Introduction) describes the main motivations and intentions of this book. Chapter 2 is a selfcontained introduction into Morreyspaces. Chapter 3 deals with hybrid smoothness spaces (which are between local and global spaces) in Euclidean n-space based onthe Morrey–Campanato refinement of the Lebesgue spaces. The presented approach relies on wavelet decompositions. This is appliedin Chapter 4 to linear and nonlinear heat equations in global and hybrid spaces. The obtained assertions about function spaces andnonlinear heat equations are used in the Chapters 5 and 6 to study Navier–Stokes equations in hybrid and global spaces.This book is addressed to graduate students and mathematicians having a working knowledge of basic elements of (global) functionspaces, and who are interested in applications to nonlinear PDEs with heat and Navier–Stokes equations as prototypes.Handbook of Hilbert Geometry (IRMA Lectures in Mathematics and Theoretical Physics Vol. 22)Athanase Papadopoulos (Université de Strasbourg, France) and Marc Troyanov (École Polytechnique Fédérale de Lausanne,Switzerland), EditorsISBN 978-3-03719-147-7. 2014. 460 pages. Hardcover. 17 x 24 cm. 78.00 EuroThis volume presents surveys, written by experts in the field, on various classical and the modern aspects of Hilbert geometry. They areassuming several points of view: Finsler geometry, calculus of variations, projective geometry, dynamical systems, and others. Somefruitful relations between Hilbert geometry and other subjects in mathematics are emphasized, including Teichmüller spaces, convexitytheory, Perron–Frobenius theory, representation theory, partial differential equations, coarse geometry, ergodic theory, algebraic groups,Coxeter groups, geometric group theory, Lie groups and discrete group actions.The Handbook is addressed to both students who want to learn the theory and researchers working in the area.Valuation Theory in Interaction (EMS Series of Congress Reports)Antonio Campillo (Universidad de Valladolid, Spain), Franz-Viktor Kuhlmann (University of Saskatchewan, Saskatoon, Canada) andBernard Teissier (Université de Paris Rive Gauche, France), EditorsISBN 978-3-03719-149-1. 2014. 670 pages. Hardcover. 17 x 24 cm. 98.00 EuroHaving its classical roots, since more than a century, in algebraic number theory, algebraic geometry and the theory of ordered fieldsand groups, valuation theory has seen an amazing expansion into many other areas in recent decades. Moreover, having been dormantfor a while in algebraic geometry, it has now been reintroduced as a tool to attack the open problem of resolution of singularities inpositive 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 positivecharacteristic.The book presents high quality research and survey papers and is of interest to researchers and graduate students who work in valuationtheory, as well as a general mathematical audience interested in the expansion and usefulness of the approach.Armen Sergeev (Steklov Mathematical Institute, Moscow, Russia)Lectures on Universal Teichmüller Space (EMS Series of Lectures in Mathematics)ISBN 978-3-03719-141-5. 2014. 112 pages. Softcover. 17 x 24 cm. 24.00 EuroThis book is based on a lecture course given by the author at the Educational Center of Steklov Mathematical Institute in 2011. Itis designed for a one semester course for undergraduate students, familiar with basic differential geometry, complex and functionalanalysis.The universal Teichmüller space is the quotient of the space of quasisymmetric homeomorphisms of the unit circle modulo Möbiustransformations. The first part of the book is devoted to the study of geometric and analytic properties of . It is an infinite-dimensionalKähler manifold which contains all classical Teichmüller spaces of compact Riemann surfaces as complex submanifolds which explainsthe name “universal Teichmüller space”. Apart from classical Teichmüller spaces, contains the space of diffeomorphisms of thecircle modulo Möbius transformations. The latter space plays an important role in the quantization of the theory of smooth strings.The quantization of is presented in the second part of the book. In contrast with the case of diffeomorphism space , which can bequantized in frames of the conventional Dirac scheme, the quantization of requires an absolutely different approach based on thenoncommutative geometry methods.The book concludes with a list of 24 problems and exercises which can be used during the examinations.European Mathematical Society Publishing HouseSeminar for Applied Mathematics, ETH-Zentrum SEW A27Scheuchzerstrasse 70CH-8092 Zürich, Switzerlandorders@ems-ph.orgwww.ems-ph.org