Abstracts for Barry Mazur, Clanton Visiting Mathematician, 2006-2007

2006-07

The 2006-07 Donald H. Clanton Visiting Mathematician was Dr. Barry Mazur of Harvard University. Dr. Mazur was with us on March 29, 2007. OPEN PROBLEMS ABOUT PROBABILITY DISTRIBUTIONS IN NUMBER THEORY John E. Johns Hall Room 101 March 29, 2007 4:00 PM The aim of this lecture is to discuss, in very concrete terms, the nature of a problem as originally posed by Sato and Tate four decades ago, to give a sense of why it is important, to give a hint of some wonderful recent work that has made progress towards its solution, and to discuss some open problems related to it. __________________________________________________   A MODERN VIEW OF CLASSICAL QUESTIONS IN ARITHMETIC Shaw Hall Younts Conference Center March 29, 2007 7:30 PM In how many different ways can we express a given prime number p as a sum of two square numbers? This has an elegant answer known already in the eighteenth century. Questions that are companions to this classical one have been the subject of some of the more spectacular advances in number theory in recent years. The aim of this talk is to introduce the audience to the beauty of these questions and to the (admittedly still fragmentary) answers to them that we currently have.