2010; 488 pp; hardcover ISBN10: 3037190779 ISBN13: 9783037190777 List Price: US$98 Member Price: US$78.40 Order Code: EMSEMC/2008
 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 1418, 2008, with about 1000 participants from 68 different countries. Ten plenary and thirtythree 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 twentytwo 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 socalled Brouwer lecture was presented. It is the Netherlands' 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 of what mathematics offers today. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in the lectures discussed at the 2008 5ECM. Table of Contents Invited Lectures  J. A. Carrillo and J. Rosado  Uniqueness of bounded solutions to aggregation equations by optimal transport methods
 B. Edixhoven  On the computation of the coefficients of modular forms
 M. Einsiedler  Effective equidistribution and spectral gap
 W. Lück  Survey on aspherical manifolds
 S. A. Merkulov  Wheeled props in algebra, geometry and quantization
 O. R. Musin  Positive definite functions in distance geometry
 J. Nešetřil and P. Ossona de Mendez  From sparse graphs to nowhere dense structures: decompositions, independence, dualities and limits
 J. Fuchs, T. Nikolaus, C. Schweigert, and K. Waldorf  Bundle gerbes and surface holonomy
 C. Teleman  Topological field theories in 2 dimensions
Lecture on Invitation by the KWG  D. van Dalen  The Revolution of 1907Brouwer's dissertation
Plenary Lectures  J. Bourgain  New developments in combinatorial number theory and applications
 J.F. Le Gall  Large random planar maps and their scaling limits
 F. Loeser  Geometry and nonarchimedean integrals
 M. Marcolli  Feynman integrals and motives
 N. Reshetikhin  Topological quantum field theory: 20 years later
Prize Lectures  O. Holtz and N. Shomron  Computational complexity and numerical stability of linear problems
 B. Klartag  Highdimensional distributions with convexity properties
 L. SaintRaymond  Some recent results about the sixth problem of Hilbert: hydrodynamic limits of the Boltzmann equation
 A. Smoktunowicz  Graded algebras associated to algebraic algebras need not be algebraic
 Author index
