Fields Medallists' Lectures

Michael Atiyah, Daniel Iagolnitzer

• Publisher: WSPC
• Year: 1997
• Print ISBN: 9789810231026, 9789810231026
• eBook ISBN: 9789812385215
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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. The restriction to 40 years is of marginal significance, since most mathematicians have made their mark long before this age.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 This volume does not pretend to be comprehensive, nor is it a historical document.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 22 Fields Medallists and so provides a highly interesting and varied picture.The contributions themselves represent the choice of the individual Medallists. In some cases the articles relate directly to the work for which the Fields Medals were awarded. In other cases new articles have been produced which relate to more current interests of the Medallists. This indicates that while Fields Medallists must be under 40 at the time of the award, their mathematical development goes well past this age. In fact the age limit of 40 was chosen so that young mathematicians would be encouraged in their future work.The Fields Medallists' Lectures is now available on CD-ROM. Sections can be accessed at the touch of a button, and similar topics grouped together using advanced keyword searches.

Table of contents

• CONTENTS
• PREFACE
• RECIPIENTS OF FIELDS MEDALS
• AUTOBIOGRAPHY OF LARS V. AHLFORS
• COMMENTARY ON: ZUR THEORIE DER ÜBERLAGERUNGSFLÄCHEN (1935)
• QUASICONFORMAL MAPPINGS, TEICHMÜLLER SPACES, AND KLEINIAN GROUPS
• THE WORK OF L. SCHWARTZ
• LAURENT SCHWARTZ
• CALCUL INFINITESIMAL STOCHASTIQUE
• THE WORK OF K. F. ROTH
• Klaus F. Roth
• RATIONAL APPROXIMATIONS TO ALGEBRAIC NUMBERS
• THE WORK OF R. THOM
• AUTOBIOGRAPHY OF RENÉ THOM
• HÖRMANDER'S WORK ON LINEAR DIFFERENTIAL OPERATORS
• AUTOBIOGRAPHY OF LARS HÖRMANDER
• LOOKING FORWARD FROM ICM 1962
• L'OEUVRE DE MICHAEL F. ATIYAH
• MICHAEL F. ATIYAH
• THE INDEX OF ELLIPTIC OPERATORS
• SUR LES TRAVAUX DE STEPHEN SMALE
• STEPHEN SMALE
• A SURVEY OF SOME RECENT DEVELOPMENTS IN DIFFERENTIAL TOPOLOGY
• THE WORK OF ALAN BAKER
• 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
• SERGEI NOVIKOV
• RÔLE OF INTEGRABLE MODELS IN THEDEVELOPMENT OF MATHEMATICS
• THE WORK OF DAVID MUMFORD
• AUTOBIOGRAPHY OF DAVID MUMFORD
• PATTERN THEORY: A UNIFYING PERSPECTIVE
• THE WORK OF GREGORI ALEKSANDROVITCH MARGULIS
• GRIGORII A. MARGULIS
• OPPENHEIM CONJECTURE
• THE WORK OF ALAIN CONNES
• ALAIN CONNES
• BRISURE DE SYMÉTRIE SPONTANÉE ET GÉOMÉTRIE DU POINT DE VUE SPECTRAL
• THE WORK OF W. THURSTON
• THE WORK OF SIMON DONALDSON
• SIMON K. DONALDSON
• REMARKS ON GAUGE THEORY, COMPLEX GEOMETRY AND 4-MANIFOLD TOPOLOGY
• THE WORK OF M. H. FREEDMAN
• MICHAEL H. FREEDMAN
• BETTI NUMBER ESTIMATES FOR NILPOTENT GROUPS
• THE WORK OF VAUGHAN F. R. JONES
• VAUGHAN F. R. JONES
• A POLYNOMIAL INVARIANT FOR KNOTS VIA VON NEUMANN ALGEBRAS1
• INDEX FOR SUBFACTORS
• THE WORK OF SHIGEFUMI MORI
• SHIGEFUMI MORI
• BIRATIONAL CLASSIFICATION OF ALGEBRAIC THREEFOLDS
• THE WORK OF E. WITTEN
• THE WORK OF EDWARD WITTEN
• Edward Witten
• GEOMETRY AND QUANTUM FIELD THEORY
• THE WORK OF JEAN BOURGAIN
• JEAN BOURGAIN
• HAMILTONIAN METHODS IN NONLINEAR EVOLUTION EQUATIONS
• THE WORK OF PIERRE-LOUIS LIONS
• 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
• EFIM I. ZELMANOV
• ON THE RESTRICTED BURNSIDE PROBLEM