Michael Francis Atiyah, Daniel Iagolnitzer9789812382597, 9812382593, 9812382569, 9789812382566, 9789812564856
FIELDS MEDALLISTS’ LECTURES 2nd Edition
edited by Sir Michael Atiyah (University of Edinburgh, UK) & Daniel Iagolnitzer (CEA-Saclay, France)
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 This volume does not pretend to be comprehensive, nor is it a historical document.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).
Table of contents :
Front cover……Page 1
Short title……Page 2
World Scientific Series in 20th Century Mathematics……Page 3
Title page……Page 4
Date-line……Page 5
PREFACE TO THE FIRST EDITION……Page 6
PREFACE TO THE SECOND EDITION……Page 8
RECIPIENTS OF FIELDS MEDALS……Page 10
CONTENTS……Page 12
Photo……Page 19
Biographical Notice……Page 20
Quasiconformal Mappings, Teichmuller Spaces, and Kleinian Groups……Page 22
The Work of L. Schwartz by H. Bohr……Page 36
Photo……Page 41
Biographical Notice……Page 42
Calcul Infinitesimal Stochastique……Page 44
Obituary: Kunihiko Kodaira……Page 64
Photo……Page 71
Biographical Notice……Page 72
On Kahler Varieties of Restricted Type……Page 74
The Work of K. F. Roth by H. Davenport……Page 78
Photo……Page 83
Biographical Notice……Page 84
Rational Approximations to Algebraic Numbers……Page 85
The Work of R. Thorn by H. Hopf……Page 92
Photo……Page 95
Autobiography……Page 96
Hormander’s Work on Linear Differential Operators by L. Garding……Page 102
Photo……Page 107
Autobiography……Page 108
Looking forward from ICM 1962……Page 111
L’oeuvre de Michael F. Atiyah by H. Cartan……Page 130
Photo……Page 137
Biography……Page 138
The Index of Elliptic Operators……Page 140
Sur Les Travaux de Stephen Smale by R. Thom……Page 154
Photo……Page 159
Biographical Notice……Page 160
A Survey of Some Recent Developments in Differential Topology……Page 167
The Work of Alan Baker by P. Turan……Page 182
Photo……Page 185
Biography……Page 186
Effective Methods in the Theory of Numbers……Page 187
Effective Methods in Diophantine Problems……Page 196
Effective Methods in Diophantine Problems. II……Page 208
Effective Methods in the Theory of Numbers/Diophantine Problems……Page 215
The Work of Serge Novikov by M. F. Atiyah……Page 220
Photo……Page 223
Biography……Page 224
Role of Integrable Models in the Development of Mathematics……Page 227
The Work of David Mumford by J. Tate……Page 244
Photo……Page 249
Autobiography……Page 250
Pattern Theory: A Unifying Perspective……Page 251
The Work of Gregory Aleksandrovitch Margulis by J. Tits……Page 288
Photo……Page 295
Biographical Notice……Page 296
Oppenheim Conjecture……Page 298
The Work of Alain Connes by H. Araki……Page 354
Photo……Page 363
Biographical Notice……Page 364
Brisure de Symetrie Spontanee et Geometrie du Point de vue Spectral……Page 365
The Work of W. Thurston by C. T. C. Wall……Page 398
The Work of Simon Donaldson by M. F. Atiyah……Page 402
Photo……Page 407
Biographical Notice……Page 408
Remarks on Gauge Theory, Complex Geometry and 4-Manifold Topology……Page 409
The Work of M. H. Freedman by J. Milnor……Page 430
Photo……Page 435
Biographical Notice……Page 436
Betti Number Estimates for Nilpotent Groups……Page 438
The Work of Vaughan F. R. Jones by J. S. Birman……Page 460
Photo……Page 471
Biographical Notice……Page 472
A Polynomial Invariant for Knots via von Neumann Algebras……Page 473
Index for Subfactors……Page 484
The Work of Shigefumi Mori by H. Hironaka……Page 512
Photo……Page 519
Biographical Notice……Page 520
Birational Classification of Algebraic Threefolds……Page 521
The Work of E. Witten by L. D. Faddeev……Page 536
The Work of Edward Witten by M. F. Atiyah……Page 539
Photo……Page 545
Biographical Notice……Page 546
Geometry and Quantum Field Theory……Page 548
The Work of Jean Bourgain by L. Caffarelli……Page 562
Photo……Page 565
Biographical Notice……Page 566
Hamiltonian Methods in Nonlinear Evolution Equations……Page 567
The Work of Pierre-Louis Lions by S. R. S. Varadhan……Page 580
Biographical Notice……Page 585
On Some Recent Methods for Nonlinear Partial Differential Equations……Page 589
Presentation de Jean-Christophe Yoccoz by A. Douady……Page 606
Recent Developments in Dynamics……Page 613
The Work of Efim Zelmanov by W. Feit……Page 636
Photo……Page 645
Biographical Notice……Page 646
On the Restricted Burnside Problem……Page 648
The Work of Richard Ewen Borcherds by P. Goddard……Page 658
Photo……Page 669
Biographical Notice……Page 670
What is Moonshine?……Page 671
The Work of William Timothy Gowers by B. Bollobas……Page 680
Photo……Page 689
Autobiography……Page 690
A New Proof of Szemeredi ‘s Theorem for Arithmetic Progressions of Length Four……Page 695
The Work of Maxim Kontsevich by C. H. Taubes……Page 720
Photo……Page 729
Biographical Notice……Page 730
Formal (Non)-Commutative Symplectic Geometry……Page 733
Comments on “Formal (Non)-Commutative Symplectic Geometry……Page 751
The Work of Curtis T. McMullen by J. Milnor……Page 754
Photo……Page 761
Biographical Notice……Page 762
Rigidity and Inflexibility in Conformal Dynamics……Page 763
The Work of Laurent Lafforgue by G. Laumon……Page 778
Photo……Page 784
The Work of Vladimir Voevodsky by C. Soule……Page 786
Photo……Page 791
Biographical Notice……Page 792
Open Problems in the Motivic Style Homotopy Theory, I……Page 796
Back cover……Page 824
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