Wolf prize in mathematics, vol.1

Description

The Wei-Liang Chow and Kuo-Tsai Chen Memorial Conference was proposed and held by Professor S.-S. Chern. It was devoted to memorializing those two outstanding and original mathematicians who had made significant contributions to algebraic geometry and algebraic topology, respectively. It also provided a forum for leading mathematicians to expound and discuss their views on new ideas in these fields, as well as trends in 21st-century mathematics. About 100 mathematicians participated in the conference, including Sir Michael Atiyah, Jacob Palis, Phillip Griffiths, David Eisenbud, Philippe Tondeur, Yujiro Kawamata, Tian Gang, and others. This volume contains selected papers presented at the conference. The topics include canonical maps of Gorenstein three-folds, fundamental groups of algebraic curves, Chen's interated integrals, algebraic fibre spaces, and more Lars V. Ahlfors / F. W. Gehring -- Ahlfors' Preface to his Collected Papers 7 -- Caratheodory's Report on Ahlfors' Work for the Fields Medal at the ICM in Oslo 1936 11 -- Ahlfors' Address as Honorary President at the Opening of the ICM in Berkeley 1986 14 -- An Extension of Schwarz's Lemma 15 -- Quasiconformal Reflections 21 -- Finitely Generated Kleinian Groups 32 -- Henri Cartan -- Breve analyse des travaux 51 -- Les Seminaires Cartan (allocution prononcee par J.-P. Serre en 1975) 62 -- Varietes analytiques complexes et cohomologie 67 -- Espaces fibres et groupes d'homotopie. I. Constructions generales / J.-P. Serre 82 -- Espaces fibres et groupes d'homotopie. II. Applications / J.-P. Serre 85 -- Discours prononce le ler fevrier 1977 a l'occasion de la remise de la Medaille d'Or du C.N.R.S. 88 -- Lennart A. E. Carleson -- Lennart Carleson's Work in Analysis / P. W. Jones 96 -- Lennart Carleson's Work in Statistical Mechanics and Dynamical Systems / M. Benedicks 108 -- On Convergence and Growth of Partial Sums of Fourier Series 120 -- Shiing-Shen Chern -- My Mathematical Education 154 -- S. S. Chern as Geometer and Friend / A. Weil 169 -- Abzahlungen fur Gewebe 173 -- A Simple Intrinsic Proof of the Gauss-Bonnet Formula for Closed Riemannian Manifolds 181 -- On Finsler Geometry 187 -- Ennio De Giorgi / M. Miranda -- Ennio de Giorgi (1928-1996) / J.-L. Lions, F. Murat 192 -- De Giorgi's Summer Holidays and XIX Hilbert Problem / M. Miranda 206 -- Alcune applicazioni al Calcolo delle variazioni di una teoria della misura K-dimensionale 207 -- Minimal Cones and the Bernstein Problem / E. Bombieri, E. Giusti 208 -- New Problems in [Gamma]-convergence and G-convergence 234 -- Samuel Eilenberg / W. S. Massey -- Samuel Eilenberg (1913-1998) / H. Bass, H. Cartan, P. Freyd, A. Heller, S. MacLane 242 -- Natural Isomorphisms in Group Theory / S. MacLane 256 -- Singular Homology Theory 263 -- Axiomatic Approach to Homology Theory / N. E. Steenrod 288 -- Paul Erdos / B. Bollobas -- The Life and Work of Paul Erdos / B. Bollobas 292 -- Selected Publications of Paul Erdos 316 -- The Gaussian Law of Errors in the Theory of Additive Number Theoretic Functions / M. Kac 328 -- The Product of Consecutive Integers is Never a Power / J. L. Selfridge 333 -- Friedrich Hirzebruch -- Bibliography after 1987 344 -- Curriculum vitae mathematicae / H. Grauert, G. Harder, R. Remmert 345 -- Friedrich Hirzebruch -- An Appreciation / M. F. Atiyah 347 -- On Steenrod's Reduced Powers, The Index of Inertia, and the Todd Genus 352 -- Arithmetic Genera and the Theorem of Riemann-Roch for Algebraic Varieties 358 -- Riemann-Roch Theorems for Differentiable Manifolds / M. F. Atiyah 363 -- Learning Complex Analysis in Munster-Paris, Zurich and Princeton from 1945 to 1953 369 -- Kunihiko Kodaira: Mathematician, Friend, and Teacher 382 -- Wolf Prize Ceremony The Knesset 389 -- Opening Speech, ICM Berlin 1998 390 -- Lars Hormander -- My Mathematical Education 404 -- On the Theory of General Partial Differential Operators 410 -- Differential Equations without Solutions 500 -- Hypoelliptic Second Order Differential Equations 505 -- Kiyosi Ito -- Foreword in Kiyosi Ito: Selected Papers 531 -- On a Formula Concerning Stochastic Differentials 540 -- Multiple Wiener Integral 551 -- The Brownian Motion and Tensor Fields on Riemannian Manifold 564 -- Stochastic Differentials 568 -- Joseph B. Keller -- Biographical Sketch 578 -- Publication List 579 -- Geometrical Theory of Diffraction 599 -- Corrected Bohr-Sommerfeld Quantum Conditions for Nonseparable Systems 614 -- Kunihiko Kodaira / Y. Miyaoka, K. Ueno -- Life of Kunihiko Kodaira / Y. Miyaoka, K. Ueno 623 -- On a Differential-Geometric Method in the Theory of Analytic Stacks 653 -- On Compact Analytic Surfaces 659 -- Robert Langlands -- Problems in the Theory of Automorphic Forms 679 -- Jean Leray / P. Malliavin -- Jean Leray Works / P. Malliavin 706 -- Biographie de Jean Leray / P. Malliavin 709 -- Sur le mouvement d'un fluide visqueux emplissant l'espace (introduction only) 711 -- Topologie et equations fonctionnelles / J. Schauder 715 -- Sur un probleme de representation conforme pose par la theorie de Helmholtz / A. Weinstein 718 -- L'anneau d'homologie d'une representation 721 -- Structure de l'anneau d'homologie d'une representation 724 -- Proprietes de l'anneau d'homologie de la projection d'un espace fibre sur sa base 727 -- Determination, dans les cas non exceptionnels, de l'anneau de cohomologie de l'espace homogene quotient d'un groupe de Lie compact par un sous-groupe de meme rang 730 -- Prolongement de la transformation de Laplace 733 -- La theorie des residus sur une variete analytique complexe 741 -- La calcul differentiel et integral sur une variete analytique complexe 746 -- Systeme d'equations aux derivees partielles a caracteristiques multiples: probleme de Cauchy ramifie; hyperbolicite partielle (introduction only) / Y. Hamada, C. Wagschal 753 -- Prolongements analytiques de la solution du probleme de Cauchy lineaire (introduction only) / Y. Hamada, A. Takeuchi 756