Series: Mathematics Colloquium

Date: Thursday, September 25, 2003

Time: 4:30 - 5:30 PM

Place: 102 McAllister Building

Host: George Andrews

Refreshments: 4:00 - 4:30 PM, in 212 McAllister

Speaker: Ken Ono, University of Wisconsin

Title: Groups Associated to Quadratic Fields 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.