THE MATHEMATICS OF SOLITAIRE

Persi Diaconis, Stanford University

It is one of the embarrassments of applied probability that we cannot usefully analyze ordinary solitaire. David Aldous and I have studied a simple version with links to random matrix theory, Toeplitz operators, algebraic combinatorics and Riemann Hilbert problems. These solve a simple case but the real problems remain open.

RANDOM WALK AND HECKE ALGEBRAS

Persi Diaconis (Stanford University)

Analysis of widely used algorithms such as the Metropolis algorithm for the Ising model can lead to very hard problems. Arun Ram and I have solved one of these using the characters of Iwahori-Hecke algebras.

NEW RELATIONS BETWEEN UNITARY MATRICES AND THE ZEROS OF RIEMANN'S ZETA FUNCTION

Persi Diaconis (Stanford University)

Typical unitary matrices show remarkable patterns in their eigenvalues. Using a new ``wrapping technique'', Marc Coram and I find the same patterns in the zeros of the zeta function. This raises novel problems in classical statistics, probability and group theory.