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Texas A&M
Title: The prime geodesic theorem
Abstract: I will discuss some recent work with K. Soundararajan on a problem with many nice interpretations. Consider the group SL(2,Z) and decompose it into conjugacy classes. The classes can be ordered by trace, and then one can ask natural questions such as: How many conjugacy classes have a given fixed trace? How many conjugacy classes have trace in a given interval (say between 1 and x with x big)? These questions are related to the sizes of class numbers for indefinite quadratic forms, and to the lengths of closed geodesics on the modular surface SL(2,Z)\H.