Ebook: First European Congress of Mathematics : Paris, July 6-10, 1992 Volume I Invited Lectures (Part 1)

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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Content:
Front Matter....Pages i-lxii
Front Matter....Pages 1-1
The Vassiliev Theory of Discriminants and Knots....Pages 3-29
Transparent Proofs and Limits to Approximation....Pages 31-91
Poisson Algebraic Groups and Representations of Quantum Groups at Roots of 1....Pages 93-119
Gauge Theory and Four-Manifold Topology....Pages 121-151
Spectral Theory and Geometry....Pages 153-185
Pattern Theory: A Unifying Perspective....Pages 187-224
Brownian Motion and Obstacles....Pages 225-248
Geometric Quantization and Equivariant Cohomology....Pages 249-295
Front Matter....Pages 297-297
The Power of Exponentiation in Arithmetic....Pages 299-320
Subspace Arrangements....Pages 321-370
Optimal Recovery of Functions and Integrals....Pages 371-390
Existence globale et diffusion pour les mod?les discrets de la cin?tique des gaz....Pages 391-410
Sporadic Groups and String Theory....Pages 411-421
A Harmonic Analysis Approach to Problems in Nonlinear Partial Differential Equations....Pages 423-444
(Some) Old and New Results on Algebraic Surfaces....Pages 445-490
Evidence for a Cohomological Approach to Analytic Number Theory....Pages 491-510
Cauchy-Riemann Operators, Self—Duality, and the Spectral Flow....Pages 511-545
Back Matter....Pages 547-548

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Content:
Front Matter....Pages i-lxii
Front Matter....Pages 1-1
The Vassiliev Theory of Discriminants and Knots....Pages 3-29
Transparent Proofs and Limits to Approximation....Pages 31-91
Poisson Algebraic Groups and Representations of Quantum Groups at Roots of 1....Pages 93-119
Gauge Theory and Four-Manifold Topology....Pages 121-151
Spectral Theory and Geometry....Pages 153-185
Pattern Theory: A Unifying Perspective....Pages 187-224
Brownian Motion and Obstacles....Pages 225-248
Geometric Quantization and Equivariant Cohomology....Pages 249-295
Front Matter....Pages 297-297
The Power of Exponentiation in Arithmetic....Pages 299-320
Subspace Arrangements....Pages 321-370
Optimal Recovery of Functions and Integrals....Pages 371-390
Existence globale et diffusion pour les mod?les discrets de la cin?tique des gaz....Pages 391-410
Sporadic Groups and String Theory....Pages 411-421
A Harmonic Analysis Approach to Problems in Nonlinear Partial Differential Equations....Pages 423-444
(Some) Old and New Results on Algebraic Surfaces....Pages 445-490
Evidence for a Cohomological Approach to Analytic Number Theory....Pages 491-510
Cauchy-Riemann Operators, Self—Duality, and the Spectral Flow....Pages 511-545
Back Matter....Pages 547-548
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