Wolf Prize in Mathematics

The following sections are included:

• List of Wolf Prize Winners

• Preface

• Contents

The following sections are included:

• Curriculum Vitae
  • Born
  • Degrees
  • Positions Held
  • Visiting Appointments
  • Prizes
  • Memberships

• PUBLICATIONS OF LARS V. AHLFORS

• Ahlfors' Preface to his Collected Papers

• Carathéodory's Report on Ahlfors' work for the Fields Medal at the ICM in Oslo 1936

• Ahlfors' Address as Honorary President at the opening of the ICM in Berkeley 1986

• AN EXTENSION OF SCHWARZ'S LEMMA
  • THE FUNDAMENTAL INEQUALITY
  • SCHOTTKY'S THEOREM
  • BLOCH'S THEOREM

• QUASICONFORMAL REFLECTIONS
  • Part I
  • Part II
  • References

• FINITELY GENERATED KLEINIAN GROUPS
  • Introduction
  • The Poincaré metric
  • Quadratic differentials
  • Beltrami differentials
  • The Fuchsian case
  • The general case
  • Direct characterization of N(Γ)
  • Invariant regions

The following sections are included:

• Curriculum Vitae

• Brève analyse des travaux
  • Fonctions analytiques
  • Topologie algébrique
  • Théorie du potential ([70], [71], [72], [73], [74], [75], [84])
  • Algèbre homologique
  • Divers
  • Collaboration au Traité de N. BOURBAKI

• Les Séminaires CARTAN

• Variétés analytiques complexes et cohomologie
  • FAISCEAUX SUR UN ESPACE TOPOLOGIQUE
  • SOUS-FAISCEAU, HOMOMORPHISME, FAISCEAU-QUOTIENT
  • COHOMOLOGIE À COEFFICIENTS DANS UN FAISCEAU
  • VARIÉTÉS ANALYTIQUES COMPLEXES; PROBLÈME ADDITIF DE COUSIN
  • FAISCEAUX ANALYTIQUES COHÉRENTS
  • VARIÉTÉS DE STEIN
  • ENONCÉ DES THÉORÈMES FONDAMENTAUX
  • APPLICATIONS
  • EXTENSIONS DIVERSES; PROBLÈMES NON RÉSOLUS
  • Bibliographie

• Espaces fibrés et groupes d'homotopie. I. Constructions générales

• Espaces fibrés et groupes d'homotopie. II. Applications

• DISCOURS DE MONSIEUR HENRI CARTAN

The following sections are included:

• CURRICULUM VITAE
  • UTBILDNING
  • ANSTÄLLNINGAR
  • ANDRA BEFATTNINGAR
  • MEDLEMSKAP I VETENSKAPLIGA SÄLLSKAP

• BlBLIOGRAFI

• Lennart Carleson's work in Analysis
  • Introduction
  • Complex Analysis
  • Fourier Analysis
  • Quasiconformal Mappings
  • Harmonic Measure
  • Selected Recent Work
  • Some Remarks
  • Selected Works of Lennart Carleson
  • References

• Lennart Carleson's work in Statistical mechanics and Dynamical systems
  • Statistical Mechanics
    • Boltzmann's theory for gases
    • Gibbs's theory for the harmonic oscillator
    • A statistical mechanical approach to Szegö's asymptotical formula for Toeplitz determinants
    • Phase transitions in Statistical Mechanics
  • Dynamical systems
    • Real dynamical systems
    • Complex Dynamical Systems
  • Acknowledgement
  • References

• ON CONVERGENCE AND GROWTH OF PARTIAL SUMS OF FOURIER SERIES
  • Introduction
  • Some notations and lemmas
  • Construction of the exceptional set
  • Estimate of the exceptional set
  • Proof of Theorem (a)
  • Summary of proof of (c)
  • The polynomials P_k(x, ω)
  • Allowed pairs p^*
  • The coverings Ω(p^*; l) and the exceptional set
  • Proof of Theorem (c). Three propositions
  • Proof of Theorem (c), completed
  • Theorem (b)
  • References

The following sections are included:

• CURRICULUM VITAE
  • Born
  • Nationality
  • Degrees
  • Positions Held
  • Honorary Professorships
  • Visiting Professorships
  • Memberships
  • Prizes

• Bibliography of the Publications of S.S. Chern
  • Books and Monographs
  • Papers
  • Collected Works

• My Mathematical Education
  • Early Education in China
  • European Student Life
  • Mathematical Isolation
  • Princeton Sunshine
  • Mathematics at the Midway
  • Settlement on the West Coast
  • Something to Play With in My Eighties
  • References

• S. S. Chern as Geometer and Friend

• Abzählungen für Gewebe
  • Der allgemeine Fall
  • Die Ausnahmefälle
  • Beispiele für Gewebe höchsten Ranges

• A SIMPLE INTRINSIC PROOF OF THE GAUSS-BONNET FORMULA FOR CLOSED RIEMANNIAN MANIFOLDS
  • Introduction
  • Résumé of some fundamental formulas in Riemannian Geometry
  • The space of unit vectors and a formula for Ω
  • Proof of the Gauss-Bonnet formula
  • REFERENCES

• On Finsler Geometry

The following sections are included:

• Ennio De Giorgi (1928–1996)
  • Minimal Surfaces and Geometric Measure Theory
  • Regularity of Solutions of Elliptic Equations
  • General Theory of Partial Differential Equations
  • Γ-Convergence
  • Logic and the Foundations of Mathematics

• Bibliography

• De Giorgi's Summer Holidays and XIX Hilbert Problem

• Alcune applicazioni al Calcolo delle variazioni di una teoria della misura K-dimensionale

• Minimal Cones and the Bernstein Problem
  • Introduction
  • Functions of Least Gradient and Oriented Boundaries of Least Area
  • Proof of Theorem A
  • Proof of Theorem B
  • Appendix
  • References

• New Problems in Γ-convergence and G-convergence
  • Obstacles
  • Local Minima
  • Evolution Problems
  • Hyperbolic Problems
  • References

The following sections are included:

• Samuel Eilenberg (1913–1998)
  • Henri Cartan
  • Saunders Mac Lane
  • Alex Heller
  • Peter Freyd
  • Hyman Bass
  • References

• Published Works of Samuel Eilenberg
  • Books
  • Papers

• NATURAL ISOMORPHISMS IN GROUP THEORY
  • Introduction
  • Functors
  • Examples
  • Equivalence of Functors
  • Examples of Natural Equivalence
  • Generalizations

• SINGULAR HOMOLOGY THEORY
  • ABSTRACT COMPLEXES
    • Closure finite complexes
    • Homology groups
    • Cohomology groups
    • Chain transformations
    • Chain homotopy
    • Chain equivalences
  • SlMPLICIAL COMPLEXES
    • The complexes k(P) and K(P)
    • The chain transformation α
    • The join
    • Proof of Theorem 9.1
    • Proper and degenerate chains
  • SINGULAR HOMOLOGIES IN A SPACE
    • The singular complex S(X)
    • The invariance theorem
    • Continuous mappings
    • Prisms
    • Homotopy
    • Relative homologies
  • PRODUCTS
    • Augmentable complexes
    • The cup product
    • The cap product
    • Chain transformations preserving products
    • Products in S(X), K(P) and k(P)
    • Commutativity of the products

• AXIOMATIC APPROACH TO HOMOLOGY THEORY
  • Introduction
  • Preliminaries
  • Basic Concepts
  • Axioms
  • Uniqueness
  • Existence
  • Generalizations

The following sections are included:

• The Life and Work of Paul Erdös
  • Acknowledgements
  • Bibliography

• SELECTED PUBLICATIONS OF PAUL ERDÖS

• THE GAUSSIAN LAW OF ERRORS IN THE THEORY OF ADDITIVE NUMBER THEORETIC FUNCTIONS

• THE PRODUCT OF CONSECUTIVE INTEGERS IS NEVER A POWER
  • Introduction
  • Basic lemmas
  • The case I > 2
  • The case I = 2
  • Remarks and further problems
  • REFERENCES

The following sections are included:

• Preliminary Remarks

• Bibliography

• Curriculum vitae mathematicae

• FRIEDRICH HIRZEBRUCH — AN APPRECIATION
  • Introduction
  • The Riemann-Roch Theorem
  • Characteristic Classes
  • Number Theory
  • Style
  • The Arbeitstagung
  • The Max Planck Institute

• ON STEENROD'S REDUCED POWERS, THE INDEX OF INERTIA, AND THE TODD GENUS
  • Introduction
  • Multiplicative Γ-Sequences
  • Reduced Powers
  • The Index
  • The Todd Genus

• ARITHMETIC GENERA AND THE THEOREM OF RIEMANN-ROCH FOR ALGEBRAIC VARIETIES
  • Introduction
  • The Main Theorem and Some of Its Consequences
  • A Sketch of the Proof of the Main Theorem
  • Remark

• RIEMANN-ROCH THEOREMS FOR DIFFERENTIABLE MANIFOLDS
  • Introduction
  • Definitions
  • Statement of results
  • Outline of proof
  • REFERENCES

• LEARNING COMPLEX ANALYSIS IN MÜNSTER-PARIS, ZÜRICH AND PRINCETON FROM 1945 TO 1953

• Kunihiko Kodaira: Mathematician, Friend, and Teacher

• WOLF PRIZE CEREMONY THE KNESSET

• OPENING CEREMONY

The following sections are included:

• Curriculum Vitae
  • University Education
  • Employment
  • Professional Honors and Positions

• Bibliography

• My Mathematical Education

• ON THE THEORY OF GENERAL PARTIAL DIFFERENTIAL OPERATORS
  • PREFACE
  • Differential Operators from an Abstract Point of View
    • Introduction
    • Definitions and results from the abstract theory of operators
    • The definition of differential operators
    • Cauchy data and boundary problems
  • Minimal Differential Operators with Constant Coefficients
    • Introduction
    • Notations and formal properties of differential operators with constant coefficients
    • Estimates by Laplace transforms
    • The differential operators weaker than a given one
    • The algebra of energy integrals
    • Analytical properties of energy integrals
    • Estimates by energy integrals
    • Some special cases of Theorem 2.2
    • The structure of the minimal domain
    • Some theorems on complete continuity
    • On some sets of polynomials
    • Remarks on the case of non-bounded domains
  • Maximal Differential Operators with Constant Coefficients
    • Introduction
    • Comparison of the domains of maximal differential operators
    • The existence of null solutions
    • Differential operators of local type
    • Construction of a fundamental solution of a complete operator of local type
    • Proof of Theorem 3.3
    • The differentiability of the solutions of a complete operator of local type
    • Spectral theory of complete self-adjoint operators of local type
    • Examples of operators of local type
    • An approximation theorem
  • Differential Operators with Variable Coefficients
    • Introduction
    • Preliminaries
    • Estimates of the minimal operator
  • References

• Differential Equations without Solutions
  • Introduction
  • The basic constructions
  • Proof of Theorem 1
  • References

• HYPOELLIPTIC SECOND ORDER DIFFERENTIAL EQUATIONS
  • Introduction
  • A necessary condition for hypoellipticity
  • Preliminaries for the proof of Theorem 1.1
  • Differentiability along noncommuting vector fields
  • Smoothing and estimates
  • References

The following sections are included:

• Vita

• Foreword

• Bibliography of Kiyosi Itô

• ON A FORMULA CONCERNING STOCHASTIC DIFFERENTIALS
  • Definitions
  • Preliminary properties of stochastic integrals
  • A formula concerning stochastic differentials
  • REFERENCES

• Multiple Wiener Integral
  • Normal random measure
  • Definition of multiple Wiener integral
  • Relation between multiple Wiener integrals and Hermite polynomials
  • Orthogonal development of L₂-functionals of β by multiple Wiener integrals
  • The case of a brownian motion process

• THE BROWNIAN MOTION AND TENSOR FIELDS ON RIEMANNIAN MANIFOLD
  • Introduction
  • The paths of the Brownian motion on a Riemannian manifold
  • The parallel displacement along the Brownian paths
  • Heat equation
  • REFERENCES

• Stochastic Differentials
  • The Space of Stochastic Differentials
  • Stochastic Differential Equations
  • Examples of Stochastic Calculus
  • References

The following sections are included:

• Curriculum Vitae of Joseph B. Keller
  • Position, Address, Personal Data
  • Education
  • Positions
  • Selected Honors

• Biographical Sketch of Joseph B. Keller

• Publication List of Joseph B. Keller

• Geometrical Theory of Diffraction
  • INTRODUCTION
  • EDGE-DIFFRACTED RAYS
  • FIELDS DIFFRACTED BY STRAIGHT EDGES
  • FIELDS DIFFRACTED BY CURVED EDGES
  • CORNER OR TIP DIFFRACTION
  • SURFACE-DIFFRACTED RAYS
  • FURTHER DEVELOPMENTS

• Corrected Bohr-Sommerfeld Quantum Conditions for Nonseparable Systems
  • INTRODUCTION
  • ASYMPTOTIC SOLUTION OF THE SCHRÖDINGER EQUATION
  • THE QUANTUM CONDITIONS
  • THE “CLASSICAL Ψ FUNCTION”
  • AN EXAMPLE—THE HARMONIC OSCILLATOR
  • REFERENCES

The following sections are included:

• LIFE OF KUNIHIKO KODAIRA
  • FIRST SIGNS OF INTEREST IN MATHEMATICS AND MUSIC
  • STUDENT AT TOKYO IMPERIAL UNIVERSITY
  • A YOUNG RESEARCHER IN A TROUBLED PERIOD
  • MARRIAGE
  • THE FIRST THREE YEARS IN THE UNITED STATES
  • HARMONIC INTEGRALS ON COMPACT COMPLEX MANIFOLDS
  • PRIME YEARS AT PRINCETON
  • DEPARTURE FROM PRINCETON
  • RETURN TO JAPAN
  • LATER YEARS
  • BIBLIOGRAPHY
    • Research Papers
    • Books
  • ACKNOWLEDGEMENT

• ON A DIFFERENTIAL-GEOMETRIC METHOD IN THE THEORY OF ANALYTIC STACKS
  • Introduction
  • Harmonic Forms with Coefficients in Complex Line Bundles
  • An Inequality

• On Compact Analytic Surfaces
  • REFERENCES

The following sections are included:

• BIBLIOGRAPHY
  • MISCELLANEOUS PUBLICATIONS
  • EDITOR

• Problems in the Theory of Automorphic Forms
  • References

The following sections are included:

• Jean Leray Works
  • Bibliography

• Biographie de Jean Leray

• Sur le mouvement d'un fluide visqueux emplissant l'espace
  • Introduction

• Topologie et équations fonctionnelles

• Sur un problème de représentation conforme posé par la théorie de Helmholtz

• L'anneau d'homologie d'une représentation

• Structure de l'anneau d'homologie d'une représentation

• Proprétés de l'anneau d'homologie de la projection d'un espace fibré sur sa base

• Détermination, dans les cas non exceptionnels, de l'anneau de cohomologie de l'espace homogène quotient d'un groupe de Lie compact par un sous-groupe de même rang

• Prolongement de la transformation de Laplace
  • BIBLIOGRAPHIE

• La théorie des résidus sur une variété analytique complexe

• Le calcul différentiel et intégral sur une variétéi analytique complexe

• Systèmes d'équations aux dérivées partielles à caractéristiques multiples: probléme de Cauchy ramifié; hyperbolicité partielle
  • INTRODUCTION

• Prolongements analytiques de la solution du problème de Cauchy linéaire
  • Introduction