Groups and Dynamics Seminar

Date: October 19, 2022

Time: 3:00PM - 4:00PM

Location: BLOC 506a

Speaker: Volodymyr Nekrashevych, Texas A&M University

Title: Dimensions of self-similar groups (part 2)

Abstract: Every contracting self-similar group defines the associated limit space with a natural class of metrics on it. If the group is the iterated monodromy group of a locally expanding covering map of a compact metric space X, then the limit space is canonically homeomorphic to X. For example, the Julia set of a sub-hyperbolic rational function is the limit space of its iterated monodromy group (where the usual metric on the Riemann sphere belongs to the above mentioned natural class of metrics on the limit space). We will discuss how the topological dimension of the limit space can be interpreted in terms of the action of the group on the rooted tree. We will also discuss possible applications of the Ahlfors-regular dimension of the limit space (for the natural class of metrics).