Michael Bersudsky
The Ohio State University
Title
Equidistribution of polynomially bounded o-minimal curves in homogenous spaces
Abstract
I will present my recent joint work with Nimish Shah and Hao Xing. We study a basic question concerning the limiting distribution of averages along unbounded curves in homogeneous spaces. We consider the class of curves which are definable in o-minimal structures, and our main result provides a natural sharp condition on this family such that the associated averages always converge to a periodic measure. Our results extend Ratner's equidistribution theorem for one-parameter unipotent flows, generalize Shah's results for polynomial curves and generalize some of the recent results Peterzil and Starchenko. Our main novelty in the proof is a certain growth property of families of functions definable in polynomially bounded o-minimal structures.
