Fields Medallists' Lectures, 2nd Edition

Michael Atiyah, Daniel Iagolnitzer

• Publisher: World Scientific
• Year: 2003
• Print ISBN: 9789812382566, 9789812382566
• eBook ISBN: 9789812564856
• Edition: 2
• Topic: Matemáticas
• Subtopic: Matemática aplicada

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 This volume does not pretend to be comprehensive, nor is it a historical document.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

• PREFACE TO THE FIRST EDITION
• PREFACE TO THE SECOND EDITION
• RECIPIENTS OF FIELDS MEDALS
• CONTENTS
• Fields Medallists' Lectures 2nd Edition
• LARS VALERIAN AHLFORS
• QUASICONFORMAL MAPPINGS, TEICHMÜLLER SPACES, AND KLEINIAN GROUPS
• THE WORK OF L. SCHWARTZ
• CALCUL INFINITESIMAL STOCHASTIQUE
• OBITUARY: KUNIHIKO KODAIRA
• ON KÄHLER VARIETIES OF RESTRICTED TYPE*
• THE WORK OF K. F. ROTH
• RATIONAL APPROXIMATIONS TO ALGEBRAIC NUMBERS
• THE WORK OF R. THOM
• HÖRMANDER'S WORK ON LINEAR DIFFERENTIAL OPERATORS
• LOOKING FORWARD FROM ICM 1962
• L'OEUVRE DE MICHAEL F. ATIYAH
• THE INDEX OF ELLIPTIC OPERATORS
• SUR LES TRAVAUX DE STEPHEN SMALE
• A SURVEY OF SOME RECENT DEVELOPMENTS IN DIFFERENTIAL TOPOLOGY
• THE WORK OF ALAN BAKER
• EFFECTIVE METHODS IN THE THEORY OF NUMBERS
• EFFECTIVE METHODS IN DIOPHANTINE PROBLEMS
• EFFECTIVE METHODS IN DIOPHANTINE PROBLEMS. II
• EFFECTIVE METHODS IN THE THEORY OF NUMBERS / DIOPHANTINE PROBLEMS
• THE WORK OF SERGE NOVIKOV
• RÔLE OF INTEGRABLE MODELS IN THE DEVELOPMENT OF MATHEMATICS
• THE WORK OF DAVID MUMFORD
• PATTERN THEORY: A UNIFYING PERSPECTIVE
• THE WORK OF GREGORY ALEKSANDROVITCH MARGULIS
• OPPENHEIM CONJECTURE
• THE WORK OF ALAIN CONNES
• BRISURE DE SYMÉTRIE SPONTANÉE ET GÉOMÉTRIE DU POINT DE VUE SPECTRAL
• THE WORK OF W. THURSTON
• THE WORK OF SIMON DONALDSON
• REMARKS ON GAUGE THEORY, COMPLEX GEOMETRY AND 4–MANIFOLD TOPOLOGY
• THE WORK OF M. H. FREEDMAN
• BETTI NUMBER ESTIMATES FOR NILPOTENT GROUPS
• THE WORK OF VAUGHAN F. R. JONES
• A POLYNOMIAL INVARIANT FOR KNOTS VIA VON NEUMANN ALGEBRAS¹
• INDEX FOR SUBFACTORS
• THE WORK OF SHIGEFUMI MORI
• BIRATIONAL CLASSIFICATION OF ALGEBRAIC THREEFOLDS
• THE WORK OF E. WITTEN
• THE WORK OF EDWARD WITTEN
• GEOMETRY AND QUANTUM FIELD THEORY
• THE WORK OF JEAN BOURGAIN
• HAMILTONIAN METHODS IN NONLINEAR EVOLUTION EQUATIONS
• THE WORK OF PIERRE-LOUIS LIONS
• ON SOME RECENT METHODS FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
• PRÉSENTATION DE JEAN-CHRISTOPHE YOCCOZ
• RECENT DEVELOPMENTS IN DYNAMICS
• THE WORK OF EFIM ZELMANOV
• ON THE RESTRICTED BURNSIDE PROBLEM
• THE WORK OF RICHARD EWEN BORCHERDS
• WHAT IS MOONSHINE?
• THE WORK OF WILLIAM TIMOTHY GOWERS
• A NEW PROOF OF SZEMERÉDI'S THEOREM FOR ARITHMETIC PROGRESSIONS OF LENGTH FOUR*
• THE WORK OF MAXIM KONTSEVICH
• FORMAL (NON)-COMMUTATIVE SYMPLECTIC GEOMETRY
• COMMENTS ON "FORMAL (NON)-COMMUTATIVE SYMPLECTIC GEOMETRY"
• THE WORK OF CURTIS T. McMULLEN
• RIGIDITY AND INFLEXIBILITY IN CONFORMAL DYNAMICS
• THE WORK OF LAURENT LAFFORGUE
• THE WORK OF VLADIMIR VOEVODSKY
• OPEN PROBLEMS IN THE MOTIVIC STABLE HOMOTOPY THEORY, I