## Program in Probability and Its Applications

Spring Kolmogorov Lecture Series

**Michel Talagrand** *(Universite Paris VI
and Ohio State University) *

*Probability and Spin Glasses *

Thursday, April 15, 1999

Physicists have developed extremely interesting (but nonrigorous)
ideas to study mean field models for spin glasses. These ideas might offer
a way to approach several very natural and important problems of stochastic
combinatorial optimization, and point towards a whole new branch of probability
theory. We will try to describe the main problems and some of the related
issues in a non-technical way.

**J. Michael Steele** *(University of Pennsylvania)
*

*Probability Theory and Combinatorial Optimization*

Wednesday, May 5, 1999

The purpose of the talk is to provide a survey of recent results
in the application of probability theory to problems of combinatorial optimization,
like the travelling salesman problem, the minimal spanning tree problem, and
tesselations of various sorts.

The talk is intended for a general mathematical audience and
is not directed just to experts.

**Lawrence A. Shepp ** *(Rutgers University)
*

*Three Studies in Applied Probability*

Thursday, June 10, 1999

4:00 - 5:00 p.m.

Probability is central to diverse applications, including a)
tomography, b) financial modelling, and c) physics.

(a) In X-ray and functional MRI, probability enters through
Fourier transforms and a new use of wavelets allows space-time resolution
trade-off.

(b) In finance, a reasonable model of hiring and firing using
Brownian motion shows that downsizing is part of the optimal policy for a
firm.

(c) In "probabilistic" mechanics, new models allow phase transition
and other phenomena of macro-micro type to be studied. E.g., let each point
of a Poisson pattern on the line be a seed and let it grow at a uniform rate
until it touches another seed. When growth stops the chance that the origin
is not covered by a seed is (non-trivially) e^{-1}. Try it!