Ebook: European Congress of Mathematics: Barcelona, July 10–14, 2000, Volume I

This is the first volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: R. Ahlswede, V. Bach, V. Baladi, J. Bruna, N. Burq, X. Cabré, P.J. Cameron, Z. Chatzidakis, C. Ciliberto, G. Dal Maso, J. Denef, R. Dijkgraaf, B. Fantechi, H. Föllmer, A.B. Goncharov, A. Grigor'yan, M. Harris, R. Iturriaga, K. Johansson, K. Khanin, P. Koskela, H.W. Lenstra, Jr., F. Loeser, Y.I. Manin, N.S. Manton, Y. Meyer, I. Moerdijk, E.M. Opdam, T. Peternell, B.M.A.G. Piette, A. Reznikov, H. Schlichtkrull, B. Schmidt, K. Schmidt, C. Simó, B. Tóth, E. van den Ban, M.-F. Vignéras, O. Viro

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This is the first volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: R. Ahlswede, V. Bach, V. Baladi, J. Bruna, N. Burq, X. Cabr?, P.J. Cameron, Z. Chatzidakis, C. Ciliberto, G. Dal Maso, J. Denef, R. Dijkgraaf, B. Fantechi, H. F?llmer, A.B. Goncharov, A. Grigor'yan, M. Harris, R. Iturriaga, K. Johansson, K. Khanin, P. Koskela, H.W. Lenstra, Jr., F. Loeser, Y.I. Manin, N.S. Manton, Y. Meyer, I. Moerdijk, E.M. Opdam, T. Peternell, B.M.A.G. Piette, A. Reznikov, H. Schlichtkrull, B. Schmidt, K. Schmidt, C. Sim?, B. T?th, E. van den Ban, M.-F. Vign?ras, O. Viro

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This is the first volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: R. Ahlswede, V. Bach, V. Baladi, J. Bruna, N. Burq, X. Cabr?, P.J. Cameron, Z. Chatzidakis, C. Ciliberto, G. Dal Maso, J. Denef, R. Dijkgraaf, B. Fantechi, H. F?llmer, A.B. Goncharov, A. Grigor'yan, M. Harris, R. Iturriaga, K. Johansson, K. Khanin, P. Koskela, H.W. Lenstra, Jr., F. Loeser, Y.I. Manin, N.S. Manton, Y. Meyer, I. Moerdijk, E.M. Opdam, T. Peternell, B.M.A.G. Piette, A. Reznikov, H. Schlichtkrull, B. Schmidt, K. Schmidt, C. Sim?, B. T?th, E. van den Ban, M.-F. Vign?ras, O. Viro
Content:
Front Matter....Pages i-l
The Mathematics of M-Theory....Pages 1-19
Probabilistic Aspects of Financial Risk....Pages 21-36
Flags and Lattice Basis Reduction....Pages 37-51
Moduli, Motives, Mirrors....Pages 53-73
The Role of Oscillations in Some Nonlinear Problems....Pages 75-99
New Families of Solutions in N-Body Problems....Pages 101-115
Irreducible Modular Representations of a Reductive p-Adic Group and Simple Modules for Hecke Algebras....Pages 117-133
Dequantization of Real Algebraic Geometry on Logarithmic Paper....Pages 135-146
Advances on Extremal Problems in Number Theory and Combinatorics....Pages 147-175
Spectral Analysis of Nonrelativistic Quantum Electrodynamics....Pages 177-201
Spectrum and Statistical Properties of Chaotic Dynamics....Pages 203-223
Sampling in Complex and Harmonic Analysis....Pages 225-246
Lower Bounds for Shape Resonances Widths of Schr?dinger Operators....Pages 247-257
The Random Graph Revisited....Pages 259-265
Difference Fields: Model Theory and Applications to Number Theory....Pages 267-274
Geometric Aspects of Polynomial Interpolation in More Variables and of Waring’s Problem....Pages 275-287
The Calibration Method for Free Discontinuity Problems....Pages 289-316
Geometry on Arc Spaces of Algebraic Varieties....Pages 317-326
Stacks for Everybody....Pages 327-348
Multiple ?-Values, Galois Groups, and Geometry of Modular Varieties....Pages 349-359
Heat Kernels on Manifolds, Graphs and Fractals....Pages 361-392
Local Langlands Correspondences and Vanishing Cycles on Shimura Varieties....Pages 393-406
Burgers Turbulence and Dynamical Systems....Pages 407-427
Random Growth and Random Matrices....Pages 429-443
Sobolev Spaces and Quasiconformal Mappings on Metric Spaces....Pages 445-456
Understanding Skyrmions Using Rational Maps....Pages 457-467
Models for the Leaf Space of a Foliation....Pages 469-479
Multivariable Hypergeometric Functions....Pages 481-489
Contact Structures, Rational Curves and Mori Theory....Pages 491-508
Analytic Topology....Pages 509-518
Towards Ryser’s Conjecture....Pages 519-532
Self-Interacting Random Motions....Pages 533-541
Harmonic Analysis on Reductive Symmetric Spaces....Pages 543-553
....Pages 555-564