Holly Krieger : Ratner's Theorems and the Oppenheim Conjecture

Posted by Holly Krieger , part of the Graduate Number Theory Seminar.

At

Oct. 13, 2010, 3 p.m.

In

SEO 427

Abstract

I will define the necessary ingredients to understand Ratner's theorems, presented in sufficient generality to deduce the Oppenheim Conjecture. Some generalizations and the quantitative version of the Oppenheim conjecture will be explored. No background in ergodic theory or quadratic forms will be assumed, though some basic algebraic number theory and theory of algebraic groups will be helpful for the latter part of the talk.