Alex Gorodnik : Rational points on algebraic varieties and homogeneous flows

Posted by Alexander Furman , part of the Departmental Colloquium.

At

Dec. 4, 2006, 3 p.m.

In

SEO 636

Abstract

We start with a discussion of some fundamental conjectures in arithmetic geometry that describe the set of solutions of Diophantine equations in terms of geometric invariants of the corresponding algebraic varieties. In particular, we mention the Batyrev-Manin conjecture on the number of rational points and the Peyre conjecture on the asymptotic distribution of rational points. We explain how to attack these conjectures in the case of homogeneous varieties using either representation theory or dynamics on homogeneous spaces.