9706670 This grant is to support a conference on Probability Theory, Ergodic Theory, and Analysis, to be held at Northwestern University in October, 1997. It will be an extension of the Midwest Probability Colloquium that has been held annually at Northwestern during the past 18 years. The conference will focus on topics from probability theory and ergodic theory that relate to almost everywhere convergence. This is an area that has been very active in the last several years, with a large increase generated by Bourgain's solution of the convergence of ergodic averages along the sequence of squares. Many important physical phenomena, as varied as the behavior of the stock market, lines in the supermarket, and data being received from a distant transmission source, exhibit locally erratic behavior which can be understood better by looking at the long term average behavior instead. The study of such stochastic processes and their connections with one another, as well as their connections in terms of their fine structure with other less random processes, is a central one in modern mathematics. It is only through such studies that we will be able to understand better and thus be able to control or predict the evolution of the physical phenomena which this mathematics can model.
