**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.