PREFACE TO THE FIRST EDITION -- PREFACE TO THE SECOND EDITION -- RECIPIENTS OF FIELDS MEDALS -- CONTENTS -- Fields Medallists' Lectures 2nd Edition -- LARS VALERIAN AHLFORS -- Reference -- QUASICONFORMAL MAPPINGS, TEICHMÜLLER SPACES, AND KLEINIAN GROUPS -- 1. Historial remarks. -- 2. Beltrami coefficients. -- 3. Extremal length. -- 4. Teichmüller's theorem. -- 5. Teichmüller spaces. -- 6. Fuchsian and quasifuchsian groups. -- 7. The Bers representation. -- 8. Kleinian groups. -- 9. The zero area problem. -- 10. Several dimensions. -- References -- THE WORK OF L. SCHWARTZ -- LAURENT SCHWARTZ (1915-2002) -- CALCUL INFINITESIMAL STOCHASTIQUE -- 1. Processus(1) -- 2. Processus à variation finie et martingales -- 2'. Martingales locales et temps d'arrêt(2) -- 3. Semi-martingales -- 4. Calcul intégral stochastique d'Ito -- 5. Le crochet(3) -- 6. Le mouvement brownien -- 7. Le calcul différential stochastique vectoriel -- la formule de changement de variables d'lto -- 8. Premiere extension: formules locales(4) -- 9. Deuxième extension: semi-martingales sur des variétés(5) de classe C² -- 10. Différentielles semi-martingales sections d'un fibré vectoriel optionnel(6) -- 11. Différents espaces tangents à une variété C²(7) -- 12. Formule d'lto et espaces tangents -- 13. Equations différentielles stochastiques (EDS) -- 14. Diffusion brownienne sur une variété -- 15. Mouvement brownien et problème de Dirichlet -- 16. Le flot d'une EDS (13.4) -- 17. Relèvement d'une semi-martingale par une connexion(8) -- 18. Semi-martingales à valeurs dans des espaces de dimension infinie(9) -- References -- OBITUARY: KUNIHIKO KODAIRA -- References -- BIOGRAPHY -- ON KÄHLER VARIETIES OF RESTRICTED TYPE* -- 1. Introduction -- 2. Proof of the Main Theorem -- 3. Applications -- References -- 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 -- Reference -- AUTOBIOGRAPHY OF LARS HÖRMANDER -- LOOKING FORWARD FROM ICM 1962 -- 1. Introduction -- 2. Pseudodifferential Operators and The Wave Front Set -- 3. Fourier Intergral Operators -- 4. Hypoellipticity -- 5. Solvability and Propagation of Singularities -- 6. Holmgren's Uniqueness Theorem -- 7. Analytic Hypoellipticity and Propagation of Analytic Singularities -- 8. Carleman Estimates -- 9. Spectral Asymptotics -- References -- L'OEUVRE DE MICHAEL F. ATIYAH -- 1. La K-théorie. -- 2. Le théorème de l'indice. -- 3. Formules de points fixes. -- Références -- MICHAEL F. ATIYAH -- THE INDEX OF ELLIPTIC OPERATORS -- Introduction -- 1. The Classical Period -- 1.1. Algebraic curves -- 1.2. Algebraic surfaces -- 1.3. Higher dimensions -- 2. Sheaf Theory -- 3. K-Theory -- 4. The Index Theorem -- References -- Postscript (1996) -- SUR LES TRAVAUX DE STEPHEN SMALE -- STEPHEN SMALE -- Bibliography -- A SURVEY OF SOME RECENT DEVELOPMENTS IN DIFFERENTIAL TOPOLOGY -- References -- THE WORK OF ALAN BAKER -- ALAN BAKER -- EFFECTIVE METHODS IN THE THEORY OF NUMBERS -- References -- EFFECTIVE METHODS IN DIOPHANTINE PROBLEMS -- 1. Introduction -- 2. On the Logarithms of Algebraic Numbers -- 3. Lower Bounds for Linear Forms -- 4. On Imaginary Quadratic Fields with Class Number 1 -- 5. On the Representation of Integers by Binary Forms -- 6. The Elliptic and Hyperelliptic Equations -- 7. On the Weierstrass Elliptic Functions -- 8. Concluding Remarks -- References -- EFFECTIVE METHODS IN DIOPHANTINE PROBLEMS. II -- 1. Introduction -- 2. Lower Bounds for Linear Forms -- 3. Diophantine Equations -- 4. Class Numbers -- 5. Elliptic Functions -- 6. Further Results and Problems -- References -- EFFECTIVE METHODS IN THE THEORY OF NUMBERS / DIOPHANTINE PROBLEMS.

References -- THE WORK OF SERGE NOVIKOV -- SERGEI NOVIKOV -- RÔLE OF INTEGRABLE MODELS IN THE DEVELOPMENT OF MATHEMATICS -- Starting as a Topologist -- The Split between Mathematics and Physics -- Learning Physics -- First Contributions to the Domain of Physics -- Modern Developments in Topology -- Integrable Models in Classical Mathematics and Mechanics -- Integrable Models in Quantum and Statistical Mechanics (1925-1965) -- Soliton Theory -- Inverse Scattering Transform -- KdV Hierarchy. Hamiltonian Properties. Generalization -- The Periodic and Quasiperiodic Problems. Riemann Surface and-Functions -- Conclusion -- THE WORK OF DAVID MUMFORD -- AUTOBIOGRAPHY OF DAVID MUMFORD -- PATTERN THEORY: A UNIFYING PERSPECTIVE -- 1.1. Introduction -- 1.2. Mathematical Formulation of the Problem -- 1.3. Four Universal Transformations of Perceptual Signals -- (i) Noise and blur. -- (ii) Superposition. -- (iii) Domain warping. -- (iv) Interruptions. -- 1.4. Pattern Analysis -- Requires Pattern Synthesis -- 1.5. Examples -- 1.5.1. Pyramids and wavelets -- 1.5.2. Segmentation as a free-boundary value problem -- 1.5.3. Random diffeomorphisms and template matching -- 1.5.4. The Stereo correspondence problem via minimum description length -- 1.6. Pattern Theory and Cognitive Information Processing -- References -- THE WORK OF GREGORY ALEKSANDROVITCH MARGULIS -- 1. Discrete subgroups of Lie groups. -- 2. The noncocompact case. Selberg's conjecture. -- 3. The cocompact case. Rigidity. -- 4. Other results. -- 4.1. S-arithmetic groups. -- 4.2. "Abstract" isomorphisms. -- 4.3. Normal subgroups. -- 4.4. Action on trees. -- 5. Conclusion. -- References -- GREGORY A. MARGULIS -- OPPENHEIM CONJECTURE -- 1. Analytic Number Theory Methods -- 1.1. Chowla's result and the distribution of values of positive definite quadratic forms at integer points.

1.2. Diagonal forms in n>5 variables. -- 1.3. A modification of the theorem of Davenport and Heilbronn. -- 1.4. Results for general quadratic forms. -- 2. Oppenheim Conjecture And Subgroup Actions On Homogeneous Spaces -- 2.1 Paper [CaS] of Cassels and Swinnerton-Dyer. -- 2.2. Paper [CaS] (continuation). -- 2.3. Closures of orbits of orthogonal groups and integer solutions of quadratic inequalities. -- 2.4. Quantitative results. -- 2.5. Markov spectrum. -- 3. Unipotent Flows On Homogeneous Spaces -- 3.1. Growth properties of polynomials. -- 3.2. Unipotent groups of linear transformations. -- 3.3. Recurrence to compact sets. -- 3.4. Finiteness of ergodic measures. -- 3.5. General properties of minimal invariant sets. -- 3.6. Topological limits of double cosets in algebraic groups. -- 3.7. Proof of Theorem 2.3.4 (a). -- 3.8. Conjectures of Dani and Raghunathan. -- 3.9. Ratner's results on unipotent flows. -- 3.10. Remarks. -- References -- THE WORK OF ALAIN CONNES -- 1. Classification of Type III Factors -- 2. Structure Analysis of Type III Factors -- 3. Classification of Automorphisms of the Hyperfinite Factor -- 4. Classification of AFD Factors -- 5. Other Works -- References -- ALAIN CONNES -- BRISURE DE SYMÉTRIE SPONTANÉE ET GÉOMÉTRIE DU POINT DE VUE SPECTRAL -- 1. Généralités -- 2. Un Calcul Infinitésimal -- 3. La Formule De L'indice Locale Et La Classe Fondamentale Transverse -- 4. La Notion De Variété Et Les Axiomes De La Géométrie -- 5. La Géométrie Spectrale De L'espace Temps -- Références -- THE WORK OF W. THURSTON -- THE WORK OF SIMON DONALDSON -- References -- SIMON K. DONALDSON -- REMARKS ON GAUGE THEORY, COMPLEX GEOMETRY AND 4-MANIFOLD TOPOLOGY -- 1. Reminiscences, 1980-83 -- 2. Gauge Theory and 4-Manifolds: Survey of Surveys -- 3. Elliptic Functions and Modular Forms -- 4. Stability and Kahler-Einstein Geometry -- References.

THE WORK OF M. H. FREEDMAN -- Papers of M. H. Freedman -- Other References -- MICHAEL H. FREEDMAN -- BETTI NUMBER ESTIMATES FOR NILPOTENT GROUPS -- 1. The Main Results -- 2. Applications to 3-Manifolds -- 3. Low-dimensional Surgery -- 4. Examples -- 5. The Proof of Theorem 2 -- 6. The Minimal Resolution -- 7. The Inequality -- Appendix A -- Appendix B -- References -- THE WORK OF VAUGHAN F. R. JONES -- 1. The Index Theorem -- 2. Knots and Links -- 3. Statistical Mechanics -- 4. Quantum Groups and Representations of Lie Algebras -- 5. Dynkin Diagrams -- 6. Concluding Remarks -- References -- VAUGHAN F. R. JONES -- A POLYNOMIAL INVARIANT FOR KNOTS VIA VON NEUMANN ALGEBRAS¹ -- Added in Proof. -- References -- INDEX FOR SUBFACTORS -- 1. Introduction -- 2. Generalities -- 2.1. The global index -- 2.2. The local index -- 2.3. Examples -- 3. The Basic Construction -- 3.1. Extending finite von Neumann algebras by subalgebras -- 3.2. Inclusions of complex semisimple algebras -- 3.3. Finite dimensional C*-algebras -- 3.4. Two extensions -- Goldman's theorem -- 4. Possible Values of the Index -- 4.1. Certain algebras generated by projections -- 4.2. Restrictions on T -- 4.3. Values of the index -- 5. The Bratteli Diagram -- the Relative Commutant -- 5.1. The Bratteli Diagram when r=1/4 -- 5.2. The Bratteli Diagrams r = 1/4 sec² -- 5.3. The relative commutant when r = 1/4 -- References -- THE WORK OF SHIGEFUMI MORI -- References -- SHIGEFUMI MORI -- BIRATIONAL CLASSIFICATION OF ALGEBRAIC THREEFOLDS -- 1. Introduction -- 2. Birational Classification -- 3. Surface Case -- 4. The Extremal Ray Theory (The Minimal Model Theory) -- 5. Applications of the Minimal Model Program (MMP) to 3-Folds -- 6. Comments on the Proofs for 3-Folds -- 7. Related Results -- (7.1) Effective Classification. -- (7.2) Differential Geometry. -- (7.3) Characteristic p.

(7.4) Mixed Characteristic Case.