Structure of Null Sets in the Plane and Applications / Giovanni Alberti, Marianna Csörnyei, David Preiss -- Some Open Questions about Symplectic 4-manifolds, Singular Plane Curves and Braid Group Factorizations / Denis Auroux -- Harmonic Measure on Fractal Sets / D. Beliaev, Stanislav Smirnov -- Singular Approximations to Hyperbolic Systems of Conservation Laws / Stefano Bianchini -- Representation Theory and Random Point Processes / Alexei Borodin, Grigori Olshanski -- Stability of Relaxation Models for Conservation Laws / François Bouchut -- Hyperbolic 3-manifolds and the Geometry of the Curve Complex / Brian H. Bowditch -- Proof of an Intersection Theorem via Fourier Analysis / Ehud Friedgut -- Nonlinear Schrödinger Equations on Compact Manifolds / Patrick Gérard -- A Probabilistic Approach to Some Problems in von Neumann Algebras / Alice Guionnet -- Singular Elements of Affine Kac–Moody Groups / Stefan Helmke, Peter Slodowy -- On the Camassa–Holm and Hunter–Saxton equations / Helge Holden -- Multiple Scales Asymptotics for Atmospheric Flows / Rupert Klein, Eileen Mikusky, Antony Owinoh -- Proof Complexity / Jan Krajícek -- Horizontal Configurations of Points in Link Complements / Daan Krammer -- Invariant Measures for Multiparameter Diagonalizable Algebraic Actions - A Short Survey / Elon Lindenstrauss -- Phase Transition Phenomena in Random Discrete Structures / Tomasz Łuczak -- Systems Controlled by Rough Paths / Terry J. Lyons -- The Stable Mapping Class Group and Stable Homotopy Theory / Jørgen Ellegaard Andersen, Michael Weiss -- A Non-asymptotic Theory for Model Selection / Pascal Massart -- Reflection, Bernoulli Numbers and the Proof of Catalan's Conjecture / Preda Mihailescu -- F-thresholds and Bernstein–Sato Polynomials / Mircea Mustaţă, Shunsuke Takagi, Kei-ichi Watanabe -- Hyperkähler Manifolds and Algebraic Geometry / Kieran G. O'Grady -- Sumsets / Imre Z. Ruzsa -- Measurable Group Theory / Yehuda Shalom -- Some Mathematical Problems of Neural Networks Theory / M. Shcherbina -- Zeroes of Gaussian Analytic Functions / Mikhail Sodin -- Painlevé's Problem, Analytic Capacity and Curvature of Measures / Xavier Tolsa -- Regularization Techniques for Singular Source Terms in Differential Equations / Anna-Karin Tornberg -- Equilibrium Measures and Polynomials / Vilmos Totik -- SLE, Conformal Restriction, Loops / Wendelin Werner -- On the Integral Points on Certain Algebraic Varieties / Umberto Zannier -- Some Problems Related with Holomorphic Functions on Tube Domains over Light Cones / Aline Bonami -- Hyperbolic PDEs, Kinetic Formulation, Geometric Measure Theory / Yann Brenier -- Random Dynamics in Spatially Extended Systems / Frank den Hollander -- Analysis and Operators 2000-2004 - Four Years of Network Activity / Jean Esterle -- Analysis of the Bottom of the Spectrum of Schrödinger Operators with Magnetic Potentials and Applications / Bernard Helffer -- Mathematical Aspects of Quantum Chaos / J.P. Keating -- The Research Training Network “Algebraic Combinatorics in Europe” / Christian Krattenthaler -- Algebras with Involution and Adjoint Groups / Marina Monsurrò -- Constructing Algebraic Varieties via Commutative Algebra / Miles Reid -- Mathematical Problems of Large Quantum Systems / Ryszard Nest -- The Grothendieck-Teichmüller Group and Galois Theory of the Rational Numbers – European Network GTEM / Jakob Stix -- Hydrodynamic Limits / François Golse -- Mathematical Aspects of Mean Field Spin Glass Theory / Francesco Guerra -- Complexity Theory, Proofs and Approximation / Johan Håstad -- Random Surfaces Enumerating Algebraic Curves / Elliott H. Lieb -- On Heegaard Diagrams and Holomorphic Disks / Peter Ozsváth, Zoltán Szabó -- Emergence of Symmetry: Conformal Invariance in Scaling Limits of Random Systems / Michael H. Freedman -- Recent Progresses in Kähler and Complex Algebraic Geometry / Claire Voisin -- Isoperimetric Inequalities, Probability Measures and Convex Geometry / Franck Barthe -- Symplectic Topology and Algebraic Families / Paul Biran -- Vortices in the Ginzburg-Landau Model of Superconductivity / Sylvia Serfaty -- Validated Numerics for Pedestrians / Warwick Tucker -- From Classical to Non-commutative Iwasawa Theory: An Introduction to the GL2 Main Conjecture / Otmar Venjakob.

Restricted to subscribers:

http://www.ems-ph.org/ebooks.php

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 prize winners were independently chosen by the 4ECM Scientific Committee as plenary or invited speakers. The other five prize winners 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. Plenary lectures François Golse (Paris, France) Francesco Guerra (Roma, Italy) Johan Håstad (Stockholm, Sweden) Andrei Okounkov (Princeton, USA) Oded Schramm (Microsoft Research, USA) Zoltán Szabó (Princeton, USA) Claire Voisin (Paris, France) Invited Lectures Giovanni Alberti (Pisa, Italy) Denis Auroux (MIT, USA and Palaiseau, France) Stefano Bianchini (Rome, Italy) François Bouchut (Paris, France) Brian Bowditch (Southampton, UK) Ehud Friedgut (Jerusalem, Israel) Patrick Gérard (Orsay, France) Alice Guionnet (Lyon, France) Stefan Helmke (Kyoto, Japan) Helge Holden (Trondheim, Norway) Rupert Klein (Berlin, Germany) Jan Krajícek (Prague, Czech Republic) Daan Krammer (Warwick, UK) Elon Lindenstrauss (Clay Mathematics Institute, USA) Tomas...