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 2010; 488 pp; hardcover ISBN-10: 3-03719-077-9 ISBN-13: 978-3-03719-077-7 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 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 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 1907--Brouwer'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 non-archimedean 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 -- High-dimensional distributions with convexity properties L. Saint-Raymond -- 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