Rational Points on Algebraic Varieties and Homogeneous Flows
Abstract
I 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, I mention the Batyrev-Manin
conjecture on the number of rational points and the Peyre conjecture
on the asymptotic distribution of rational points. I explain how to attack
these conjectures in the case of homogeneous varieties using
either representation theory or dynamics on homogeneous spaces.
R E F R E S H M E N T S
4:00 to 4:25 PM
Kenneth W. Anderson
Memorial Reading Room
