This award provides support for a three-day conference on computational number theory to be held in honor of Professor A.O.L. Atkin. The conference, which will take place on September 14-16, 1995, at the University of Illinois at Chicago, will focus on two fundamental aspects of computation in number theory. The first of these concerns development of computational techniques to conduct experimentation and support conjectures in the pure theory of numbers, especially in areas related to modular forms; the second deals with applications of techniques from the pure theory to algorithmic problems such as those arising in factoring, primality testing, and counting points on algebraic varieties. This research is in the field of number theory. This subject area has its historical roots in the study of the whole numbers, addressing such questions as the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for mainly aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and the design of communication systems.
