Departmental Colloquium
Alex Gorodnik
Caltech
Rational points on algebraic varieties and homogeneous flows
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.
Monday December 4, 2006 at 3:00 PM in SEO 636