This award supports a conference entitled: "Convergence in Erogdic Theory and Probability". The conference will be held from 23 to 26 June 1993, at Ohio State University. The conference will be concerned with the behavior of averages along subsequences and weighted averages in general, which have been studied using techniques from harmonic analysis, number theory, and measure theory.. The objectives of the conference are: 1. Improve communication among researchers of these interrelated fields; 2. Stimulate additional connections the lines of investigation involved in these studies.