Thursday, July 28/1:30 PM/Grande Ballroom

The George Polya Prize

Chair: Avner Friedman, University of Minnesota, Minneapolis

The Polya Prize, established in 1969, is awarded in 1994 for a notable application of combinatorial theory made during the five to ten years preceding the award.

The 1994 recipients are Harry Kesten, Cornell University, and Gregory Chudnovsky, Columbia University.

On Some Stochastic Growth Models

The speaker will consider the asymptotic size and shape of growing aggregates on the lattice Zd. The aggregate at time n, An , is a connected set of n sites of Zd. A1 = {0} and An+1 is formed by adding a single site yn to An . yn is chosen by some random mechanism from = the boundary of An . He will concentrate on two of the best known examples: Eden's model, which has yn uniformly distributed over , and Diffusion Limited Aggregation in which yn is chosen according to harmonic measure from infinity. He will also discuss a variant of Eden's model in which the distribution of yn strongly favors those points of which have at least two neighbors in An over the points which have only one neighbor in An .

Harry Kesten, Department of Mathematics, Cornell University

Harry Kesten obtained his Ph.D. at Cornell University under the guidance of Mark Kac. Since 1962 he has been a regular faculty member in the Department of Mathematics at Cornell. Before that he had taught at Princeton University and at the Hebrew University in Jerusalem. Professor Kesten has many times been invited to give special lectures both in the U.S. and abroad; he is a Guggenheim Fellow, Alfred P. Sloan Fellow, and on the editorial boards of several mathematical publications. He has received distinguished honors like the Brouwer Memorial Lecture and Medal, and the Correspondent Royal Dutch Academy of Sciences. He is also a member of the National Academy of Sciences, USA. Professor Kesten's mathematical interests have been almost entirely in probability theory, in particular in random walk, and in models inspired by statistical mechanics.

Fast Computational Methods in Pure and Applied Mathematics

Several classes of fast approximation methods used for solution of ordinary and partial differential equations are discussed. They include: analytic continuation techniques (in multidimensional complex spaces), Riemann boundary value methods (including related monodromy and Pad‚ approximation techniques), and methods of remapping and regridding. These approximation methods are used in number-theoretic proofs of irrationality and linear independence of values of classical transcendental functions, and in many applied problems. Problems of applied mathematics under consideration include 1D, 2D, and 3D inverse scattering problems of wave (Schr”dinger) equations arising in physics and in geophysics.

Gregory V. Chudnovsky, Department of Mathematics, Columbia University

Gregory V. Chudnovsky was born in Kiev, Ukraine. In 1975 he obtained his Ph.D. from the Institute of Mathematics, Ukrainian Academy of Sciences; Maitre de Conference, Paris University, 1977-78; and Maitre de Recherche, CNRS Paris, France, 1979-81. He emigrated to the U.S. in 1978 and became a U.S. citizen. Dr. Chudnovsky has been a research scientist at Columbia University since 1978. He is an author and editor of books in number theory, computer algebra, and mathematical physics. Among the many honors and awards that he has received are the Moscow Mathematical Society Prize, Peccot-Vimont Prize - College de France, Guggenheim Fellow, and MacArthur Foundation fellowship. Dr. Chudnovsky's current fields of research interest include: computational number theory, high-performance computing and computing architecture, computer algebra, approximation methods, and inverse methods in mathematical physics.