Table of contents: Plenary Lectures • V.I. Arnold: The Vassiliev Theory of Discriminants and Knots • L. Babai: Transparent Proofs and Limits to Approximation • C. De Concini: Poisson Algebraic Groups and Representations of Quantum Groups at Roots of 1 • S.K. Donaldson: Gauge Theory and Four-Manifold Topology • W. Müller: Spectral Theory and Geometry • D. Mumford: Pattern Theory: A Unifying Perspective • A.-S. Sznitman: Brownian Motion and Obstacles • M. Vergne: Geometric Quantization and Equivariant Cohomology • Parallel Lectures • Z. Adamowicz: The Power of Exponentiation in Arithmetic • A. Björner: Subspace Arrangements • B. Bojanov: Optimal Recovery of Functions and Integrals • J.-M. Bony: Existence globale et diffusion pour les modèles discrets • R.E. Borcherds: Sporadic Groups and String Theory • J. Bourgain: A Harmonic Analysis Approach to Problems in Nonlinear Partial Differatial Equations • F. Catanese: (Some) Old and New Results on Algebraic Surfaces • Ch. Deninger: Evidence for a Cohomological Approach to Analytic Number Theory • S. Dostoglou and D.A. Salamon: Cauchy-Riemann Operators, Self-Duality, and the Spectral Flow

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