## Departmental Colloquium

Alex Furman

UIC

Dynamics on some homogeneous spaces

**Abstract:**In this talk I will discuss some classical results and recent developments in the study of such dynamical systems as automorphisms of the torus $T^d=R^d/Z^d$ or translations on $SL_d(R)/SL_d(Z)$. These very concrete systems have interesting dynamics, that have applications in Number Theory (Margulis's proof of Mahler's conjecture, the progress by Einsiedler-Katok-Lindenstrauss towards Littlewood's conjecture, etc.) In the talk we shall describe some of the known dynamical phenomena that occur in these systems.

Friday October 5, 2012 at 3:00 PM in SEO 636