1mZ2hsN

New books published by theIndividual members of the EMS, member societiesor societies with a reciprocity agreement (such asthe American, Australian and Canadian MathematicalSocieties) are entitled to a discount of 20%on any book purchases, if ordered directly at theEMS Publishing House.Benoît Grébert (Université de Nantes, France) and Thomas Kappeler (Universität Zürich, Switzerland)The Defocusing NLS Equation and Its Normal Form (EMS Series of Lectures in Mathematics)ISBN 978-3-03719-131-6. March 2014. 176 pages. Softcover. 17 x 24 cm. 32.00 EuroThe theme of this monograph is the nonlinear Schrödinger equation. This equation models slowly varying wave envelopes in dispersive media and arises in variousphysical 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 partialdifferential equation in the strongest possible sense. In particular, all solutions of the dNLS equation on the circle are periodic, quasi-periodic or almost-periodic intime 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 thesefields 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.Emmanuel Hebey (Université de Cergy-Pontoise, France)Compactness and Stability for Nonlinear Elliptic Equations (Zurich Lectures in Advanced Mathematics)ISBN 978-3-03719-134-7. 2014. 304 pages. Softcover. 17 x 24 cm. 42.00 EuroThe book offers an expanded version of lectures given at ETH Zürich in the framework of a Nachdiplomvorlesung. Compactness and stability for nonlinear ellipticequations in the inhomogeneous context of closed Riemannian manifolds are investigated, a field presently undergoing great development. The author describesblow-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, andtheories 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.Robert J. Marsh (University of Leeds, UK)Lecture Notes on Cluster Algebras (Zurich Lectures in Advanced Mathematics)978-3-03719-130-9. 2013. 132 pages. Softcover. 17 x 24 cm. 28.00 EuroThe 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 shortintroduction to reflection groups is given in order to describe this and the corresponding generalized associahedra. A discussion of cluster algebra periodicity, which hasa 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 structureof the homogeneous coordinate ring of the Grassmannian, both of which have a beautiful description in terms of combinatorial geometry.Isabelle Gallagher (Université Paris-Diderot, France), Laure Saint-Raymond (Université Pierre et Marie Curie, Paris) and Benjamin Texier (Université Paris-Diderot,France)From Newton to Boltzmann: Hard Spheres and Short-range Potentials (Zurich Lectures in Advanced Mathematics)978-3-03719-129-3. 2013. 150 pages. Softcover. 17 x 24 cm. 32.00 EuroThe 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, andcompactly 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 thenumber of particles tends to infinity and their size simultaneously goes to zero, in the Boltzmann-Grad scaling.This book is intended for mathematicians working in the fields of partial differential equations and mathematical physics, and is accessible to graduate students with abackground in analysis.Eduardo Casas-Alvero (Universitat de Barcelona, Spain)Analytic Projective Geometry (EMS Textbooks in Mathematics)ISBN 978-3-03719-138-5. 2014. 636 pages. Hardcover. 16.5 x 23.5 cm. 58.00 EuroThis book contains a comprehensive presentation of projective geometry, over the real and complex number fields, and its applications to affine and Euclideangeometries. It covers central topics such as linear varieties, cross ratio, duality, projective transformations, quadrics and their classifications – projective, affine andmetric –, as well as the more advanced and less usual spaces of quadrics, rational normal curves, line complexes and the classifications of collineations, pencils ofquadrics 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 themare 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 linearalgebra. The text is a valuable guide to graduate students and researchers working in areas using or related to projective geometry.MATHEON – Mathematics for Key Technologies (EMS Series in Industrial and Applied Mathematics, Vol. 1)Peter Deuflhard, Martin Grötschel, Frank Schmidt (all Konrad-Zuse-Zentrum, Berlin, Germany), Dietmar Hömberg, Volker Mehrmann, Martin Skutella (all TechnischeUniversität Berlin, Germany), Ulrich Horst, Jürg Kramer (both Humboldt-Universität zu Berlin, Germany), Konrad Polthier, Christof Schütte (both Freie UniversitätBerlin, Germany) and Jürgen Sprekels (Weierstraß Institut für Angewandte Analysis und Stochastik, Berlin, Germany), Editors978-3-03719-137-8. 2014. 466 pages. Hardcover. 17 x 24 cm. 48.00 EuroMathematics: intellectual endeavor, production factor, key technology, key to key technologies? Mathematics is all of these! The last three of its facets have been thefocus of the research and development in the Berlin-based DFG Research Center MATHEON in the last twelve years. Through these activities MATHEON has become aninternational trademark for carrying out creative, application-driven research in mathematics and for cooperating with industrial partners in the solution of complexproblems 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, andto explore new options. Researchers in mathematical fields such as Optimization, Discrete Mathematics, Numerical Analysis, Scientific Computing, Applied Analysisand Stochastic Analysis have to work hand in hand with scientists and engineers to fully exploit this potential and to strengthen the transversal role of mathematicsin 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 MATHEONapplication areas: Life Sciences, Networks, Production, Electronic and Photonic Devices, Finance, Visualization, and Education.European Mathematical Society Publishing HouseSeminar for Applied Mathematics, ETH-Zentrum SEW A27Scheuchzerstrasse 70CH-8092 Zürich, Switzerlandorders@ems-ph.orgwww.ems-ph.org