Series: Mathematics Colloquium

Date: Thursday, October 30, 2003

Time: 4:00 - 5:00 PM

Place: 102 McAllister Building

Host: Yuri Zarhin

Refreshments: 3:15 - 4:00 PM, in 212 McAllister

Speaker: Karl Rubin, Stanford

Title: Ranks of Elliptic Curves

Abstract:  

The rank of an elliptic curve is a measure of the number of solutions
of the equation that defines the curve.  In recent years there has
been spectacular progress in the theory of elliptic curves, but the
rank remains very mysterious.  Even basic questions such as how to
compute the rank, or whether the rank can be arbitrarily large, are
not settled.  In this lecture we will introduce elliptic curves and
discuss what is known, as well as what is conjectured but not known,
about ranks.