Tuesday, December 9
Milner 317, 4:00 PM
Title: Class groups and elliptic curves
Abstract: We consider questions related to the arithmetic of elliptic curves and quadratic number fields, two of the most basic objects in algebraic number theory and arithmetic geometry. We shall survey classical questions of Gauss, Cohen and Lenstra, Goldfeld, and Mazur on the `expected' behavior of ideal class groups, Mordell-Weil groups, and Shafarevich-Tate groups. The purpose of this lecture is to review these fundamental questions and to present recent results. The talk will be aimed at a general audience.