Fields Medallists' Lectures, 2nd Edition / Edition 2

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Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field — that of mathematics — and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes. A list of Fields Medallists and their contributions provides a bird's-eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from Fields Medallists and so provides a highly interesting and varied picture. The second edition of Fields Medallists' Lectures features additional contributions from the following Medallists: Kunihiko Kodaira (1954), Richard E Borcherds (1998), William T Gowers (1998), Maxim Kontsevich (1998), Curtis T McMullen (1998) and Vladimir Voevodsky (2002).
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Product Details

Table of Contents

Preface to the First Edition
Preface to the Second Edition
Recipients of Fields Medals
Quasiconformal Mappings, Teichmuller Spaces, and Kleinian Groups 5
Calcul Infinitesimal Stochastique 27
On Kahler Varieties of Restricted Type 57
Rational Approximations to Algebraic Numbers 68
Looking forward from ICM 1962 94
The Index of Elliptic Operators 123
A Survey of Some Recent Developments in Differential Topology 150
Effective Methods in the Theory of Numbers 170
Effective Methods in Diophantine Problems 179
Effective Methods in Diophantine Problems. II 191
Effective Methods in the Theory of Numbers/Diophantine Problems 198
Role of Integrable Models in the Development of Mathematics 210
Pattern Theory: A Unifying Perspective 234
Oppenheim Conjecture 281
Brisure de Symetrie Spontanee et Geometrie du Point de vue Spectral 348
Remarks on Gauge Theory, Complex Geometry and 4-Manifold Topology 392
Betti Number Estimates for Nilpotent Groups 421
A Polynomial Invariant for Knots via von Neumann Algebras 456
Birational Classification of Algebraic Threefolds 504
Geometry and Quantum Field Theory 531
Hamiltonian Methods in Nonlinear Evolution Equations 550
On Some Recent Methods for Nonlinear Partial Differential Equations 572
Recent Developments in Dynamics 596
On the Restricted Burnside Problem 631
What is Moonshine? 654
A New Proof of Szemeredi's Theorem for Arithmetic Progressions of Length Four 678
Formal (Non)-Commutative Symplectic Geometry 716
Comments on "Formal (Non)-Commutative Symplectic Geometry" 734
Rigidity and Inflexibility in Conformal Dynamics 746
Open Problems in the Motivic Style Homotopy Theory, I 779
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