Date & Time: Wednesday, January 18, 2015, 16:00-17:00.
Venue: Ramanujan Hall
Speaker: V. Kumar Murty, University of Toronto
Title: Rational Points on Elliptic Curves
Abstract: The classical problem of Diophantine equations is to solve polynomial equations over the rationals. More generally, we may consider solutions over an extension of the rationals. If the equations define an elliptic curve (or more generally, an Abelian variety), there is more structure. In particular, the set of rational points forms a group which is finitely generated. What happens if we consider the same problem over an infinite extension (or equivalently, over an infinite tower of extensions) ? The problem becomes very subtle and is the subject of current research. We shall describe some of the recent results in this area.