Fields Medallists' Lectures

by Atiyah, Michael Francis; Iagolnitzer, Daniel; Iagolnitzer, Daniel

• ISBN13: 9789810231026
• ISBN10: 9810231024
• Format: Hardcover
• Copyright: 1997-04-01
• Publisher: World Scientific Pub Co Inc

Summary

Although not as publicly well-known as the Nobel Prizes, the Fields Medal shares the same intellectual standing and is the equivalent award in the field of mathematics. This volume presents a selected list of 22 Fields Medallists and their contributions to give a highly interesting and varied bird's eye view of mathematics over the past 60 years. The contributions relate directly to the work for which the Medals were awarded or to the medallists' more current interests. In most cases, they are preceded by the introductory speech given by another leading mathematician during the prize ceremony, a photograph and up-to-date biographical notice.

Table of Contents

Preface	v	(1)
Recipients of Fields Medals	vi
1936 L. V. AHLFORS	3	(22)
Autobiography	3	(5)
Commentary on: Zur Theorie der Uberlagerungsflachen (1935)	8	(2)
Quasiconformal Mappings, Teichmuller Spaces, and Kleinian Groups	10	(15)
1950 L. SCHWARTZ	25	(28)
The Work of L. Schwartz	25	(6)
H. Bohr
Biographical Notice	31	(2)
Calcul Infinitesimal Stochastique	33	(20)
1958 K. F. ROTH	53	(14)
The Work of K. F. Roth	53	(6)
H. Davenport
Biographical Notice	59	(1)
Rational Approximations to Algebraic Numbers	60	(7)
R THOM	67	(10)
The Work of R. Thom	67	(4)
H. Hopf
Autobiography	71	(6)
1962 L. HORMANDER	77	(28)
Hormander's Work On Linear Differential Operators	77	(6)
L. Garding
Autobiography	83	(3)
Looking forward from ICM 1962	86	(19)
1966 M. F. ATIYAH	105	(24)
L'oeuvre de Michael F. Atiyah	105	(8)
H. Cartan
Biography	113	(2)
The Index of Elliptic Operators	115	(14)
S. SMALE	129	(28)
Sur les Travaux de Stephen Smale	129	(6)
R. Thom
Biographical Notice	135	(7)
A Survey of Some Recent Developments in Differential Topology	142	(15)
1970 A. BAKER	157	(38)
The Work of Alan Baker	157	(4)
P. Turan
Biography	161	(1)
Effective Methods in the Theory of Numbers	162	(9)
Effective Methods in Diophantine Problems	171	(12)
Effective Methods in Diophantine Problems. II. Comments	183	(7)
Effective Methods in the Theory of Numbers/Diophantine Problems	190	(5)
S. NOVIKOV	195	(24)
The Work of Serge Novikov	195	(4)
M. F. Atiyah
Biography	199	(3)
Role of Integrable Models in the Development of Mathematics	202	(17)
1974 D. MUMFORD	219	(44)
The Work of David Mumford	219	(6)
J. Tate
Autobiography	225	(1)
Pattern Theory: A Unifying Perspective	226	(37)
1978 G. A. MARGULIS	263	(66)
The Work of Gregori Aleksandrovitch Margulis	263	(8)
J. Tits
Biographical Notice	271	(1)
Oppenheim Conjecture	272	(57)
1982 A. CONNES	329	(44)
The Work of Alain Connes	329	(10)
H. Araki
Biographical Notice	339	(1)
Brisure de Symetrie Spontanee et Geometrie du Point de vue Spectral	340	(33)
W. P. THURSTON	373	(4)
The Work of W. Thurston	373	(4)
C. T. C. Wall
1986 S. K. DONALDSON	377	(28)
The Work of Simon Donaldson	377	(6)
M. F. Atiyah
Biographical Notice	383	(1)
Remarks on Gauge Theory, Complex Geometry and 4-Manifold Topology	384	(21)
M. H. FREEDMAN	405	(30)
The Work of M. H. Freedman	405	(6)
J. Milnor
Biographical Notice	411	(2)
Betti Number Estimates for Nilpotent Groups	413	(22)
1990 V. F. R. JONES	435	(52)
The Work of Vaughan F. R. Jones	435	(12)
J. S. Birman
Biographical Notice	447	(1)
A Polynomial Invariant for Knots via von Neumann Algebras	448	(11)
Index for Subfactors	459	(28)
S. MORI	487	(24)
The Work of Shigefumi Mori	487	(8)
H. Hironaka
Biographical Notice	495	(1)
Birational Classification of Algebraic Threefolds	496	(15)
E. WITTEN	511	(26)
The Work of E. Witten	511	(3)
L. D. Faddeev
The Work of Edward Witten by M. F. Atiyah	514	(7)
Biographical Notice	521	(2)
Geometry and Quantum Field Theory	523	(14)
1994 J. BOURGAIN	537	(18)
The Work of Jean Bourgain	537	(4)
L. Caffarelli
Biographical Notice	541	(1)
Hamiltonian Methods in Nonlinear Evolution Equations	542	(13)
P. L. LIONS	555	(26)
The Work of Pierre-Louis Lions	555	(5)
S. R. S. Varadhan
Biographical Notice	560	(3)
On Some Recent Methods for Nonlinear Partial Differential Equations	563	(18)
J. C. YOCCOZ	581	(30)
Presentation de Jean-Christophe Yoccoz	581	(7)
A. Douady
Recent Developments in Dynamics	588	(23)
E. I. ZELMANOV	611
The Work of Efim Zelmanov	611	(10)
W. Feit
Biographical Notice	621	(2)
On the Restricted Burnside Problem	623