Date:	Tue, October 20, 2009
Time:	14:00
Place:	Research I Seminar Room

Abstract: This is a PhD proposal defense. We will discuss two topics. The first topic deals with extending results of Grigorchuk, Kaimanovich, and Nagnibeda regarding the ergodic properties of the boundary action of a subgroup of a finitely generated free group. In particular, we are interested in what happens when the boundary is equipped with the Patterson-Sullivan measure. The second topic deals with the theory of graphed equivalence relations. We will discuss the issue of stochastic homogenization (i.e. finding invariant measures on a given family of graphs) as it relates to the space of rooted Schreier graphs. Given that Schreier graphs play a central role in the first topic, this yields a connection between the two halves of the proposal.