Groups and Operator Algebras Seminar

Speaker: Mehrdad Kalantar (University of Oxford)

Title: Growth conditions for topological freeness

Abstract: Given a finitely generated group $G$, a non-trivial element $g\in G$, and a minimal action of $G$ on a compact space $X$, with amenable stabilizers, we prove sufficient conditions in terms of various growth/decay functions for topological freeness of the action of $g$ on $X$. We apply our results to the case of the (Furstenberg) boundary action of $G$, to conclude $C^*$-simplicity under (semi)rapid decay conditions. In this context, we also give a description of the support of stationary states on the reduced $C^*$-algebra of $G$. We further extend these techniques to conclude topological freeness for more general classes of actions under growth assumptions on the $C^*$-algebras generated by unitary representations weakly containing the quasi-regular representations of the stabilizer subgroups.