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Tuesday, November 8, 2005

**Abstract:** The Birch and Swinnerton-Dyer conjecture provides a way for methods of analytic number theory to produce results on ranks of families of elliptic curves by studying properties of their L-functions. In particular, we are interested in questions such as: How many L-functions in a given family vanish (or not) at the central point? What is the average (analytic) rank of the family? In this talk I will discuss recent progress on these problems.