Date:	Fri, November 7, 2014
Time:	11:15
Place:	Seminar Room (120), Research I

Abstract: Answering a conjecture of Oppenheim, Margulis proved in 1986 that if \(Q(x_1, \dots, x_n)\) is an irrational indefinite quadratic form on \(n \ge 3\) variables, then the set of values \(Q(x_1, \dots, x_n)\) where \(x_1, \dots, x_n\) vary over the set of integers is dense in \({\mathbb R}\). Later, Eskin, Margulis, and Mozes studied the asymptotic distribution of the values of \(Q\), when \((x_1, \dots, x_n)\) varies in a ball of radius \(R\) and \(R \to \infty\). In this talk, I will briefly describe these works, explain the connection to Lie group action dynamics, and at the end report on a related joint work in progress with Seonhee Lim and Jiyoung Han.