2005; 900 pp; hardcover ISBN10: 3037190094 ISBN13: 9783037190098 List Price: US$138 Member Price: US$110.40 Order Code: EMSEMC/2004
 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, and Barcelona, 2000, the Fourth European Congress of Mathematics took place in Stockholm, Sweden, June 27 to July 2, 2004, with 913 participants from 65 countries. Apart from seven plenary and thirty three invited lectures, there were six "Science Lectures" covering the most relevant aspects of mathematics in science and technology. Moreover, twelve projects of the EU Research Training Networks in Mathematics and Information Sciences, as well as Programmes from the European Science Foundation in Physical and Engineering Sciences, were presented. Ten EMS Prizes were awarded to young European mathematicians who have made a particular contribution to the progress of mathematics. Five of the prizewinners were independently chosen by the 4ECM Scientific Committee as plenary or invited speakers. The other five prizewinners gave their lectures in parallel sessions. Most of these contributions are now collected in this volume, providing a permanent record of so much that is best in mathematics today. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians. Table of Contents Invited Speakers  G. Alberti, M. Csörnyei, and D. Preiss  Structure of null sets in the plane and applications
 D. Auroux  Some open questions about symplectic 4manifolds, singular plane curves and braid group factorizations
 D. Beliaev and S. Smirnov  Harmonic measure on fractal sets
 S. Bianchini  Singular approximations to hyperbolic systems of conservation laws in one space dimension
 A. Borodin and G. Olshanski  Representation theory and random point processes
 F. Bouchut  Stability of relaxation models for conservation laws
 B. H. Bowditch  Hyperbolic \(3\)manifolds and the geometry of the curve complex
 E. Friedgut  Proof of an intersection theorem via Fourier analysis
 P. Gérard  Nonlinear Schrödinger equations on compact manifolds
 A. Guionnet  A probabilistic approach to some problems in von Neumann algebras
 S. Helmke and P. Slodowy  Singular elements of affine KacMoody groups
 H. Holden  On the CamassaHolm and HunterSaxton equations
 R. Klein, E. Mikusky, and A. Owinoh  Multiple scales asymptotics for atmospheric flows
 J. Krajicek  Proof complexity
 D. Krammer  Horizontal configurations of points in link complements
 E. Lindenstrauss  Invariant measures for multiparameter diagonalizable algebraic actions  A short survey
 T. Luczak  Phase transition phenomena in random discrete structures
 T. Lyons  Systems controlled by rough paths
 I. Madsen and M. Weiss  The stable mapping class group and stable homotopy theory
 P. Massart  A nonasymptotic theory for model selection
 P. Mihailescu  Reflection, Bernoulli numbers and the proof of Catalan's conjecture
 M. Mustata, S. Takagi, and K. Watanabe  \(F\)thresholds and BernsteinSato polynomials
 K. G. O'Grady  Hyperkähler manifolds and algebraic geometry
 I. Z. Ruzsa  Sumsets
 Y. Shalom  Measurable group theory
 M. Shcherbina  Some mathematical problems of Neural networks theory
 M. Sodin  Zeroes of Gaussian analytic functions
 X. Tolsa  Painlevé's problem, analytic capacity and curvature of measures
 A.K. Tornberg  Regularization techniques for singular source terms in differential equations
 V. Totik  Equilibrium measures and polynomials
 W. Werner  SLE, conformal restriction, loops
 U. Zannier  On the integral points on certain algebraic varieties
Network Lectures  A. Bonami  Some problems related with holomorphic functions on tube domains over light cones
 Y. Brenier  Hyperbolic PDEs, kinetic formulation and geometric measure theory
 F. den Hollander  Random dynamics in spatially extended systems
 J. Esterle  Analysis and operators 20002004. Four years of network activity
 B. Helffer  Analysis of the bottom of the spectrum of Schrödinger operators with magnetic potentials and applications
 J. P. Keating  Mathematical aspects of quantum chaos
 C. Krattenthaler  The research training network "Algebraic Combinatorics in Europe"
 M. Monsurro  Algebras with involution and adjoint groups
 M. Reid  Constructing algebraic varieties via commutative algebra
 J. P. Solovej  Mathematical problems of large quantum systems
 J. Stix  The GrothendieckTeichmüller group and Galois theory of the rational numbers  European network GTEM
Plenary Speakers  F. Golse  Hydrodynamic limits
 F. Guerra  Mathematical aspects of mean field spin glass theory
 J. Hastad  Complexity theory, proofs and approximation
 A. Okounkov  Random surfaces enumerating algebraic curves
 P. Ozsvath and Z. Szabo  On Heegaard diagrams and holomorphic disks
 O. Schramm  Emergence of symmetry: Conformal invariance in scaling limits of random systems
 C. Voisin  Recent progresses in Kähler and complex algebraic geometry
Prize Lectures  F. Barthe  Isoperimetric inequalities, probability measures and convex geometry
 P. Biran  Symplectic topology and algebraic families
 S. Serfaty  Vortices in the GinzburgLandau model of superconductivity
 W. Tucker  Validated numerics for pedestrians
 O. Venjakob  From classical to noncommutative Iwasawa theory: An introduction to the \(GL_2\) main conjecture
 Index of authors
