# An application of Margulis' inequality to effective equidistribution.

 Informal Group Action Seminar Topic: An application of Margulis' inequality to effective equidistribution. Speaker: Asaf Katz Affiliation: University of Chicago Date: Wednesday, December 5 Time/Room: 4:00pm - 5:15pm/Simonyi Hall 101

Ratner's celebrated equidistribution theorem states that the trajectory of any point in a homogeneous space under a unipotent flow is getting equidistributed with respect to some algebraic measure. In the case where the action is horospherical, one can deduce an effective equidistribution result by mixing methods, an idea that goes back to Margulis' thesis.

When the homogeneous space is non-compact, one needs to impose further diophantine conditions'' over the base point, quantifying some recurrence rates, in order to get a quantified equidistribution result.

In the talk I will discuss certain diophantine conditions, and in particular I will show how a new Margulis' type inequality for translates of horospherical orbits helps to verify such conditions, leading to a quantified equidistribution result for a large class of points, akin to the results of A. Strombergsson regarding the SL2 case.