Groups and Dynamics Seminar
Date: March 6, 2024
Time: 3:00PM - 4:00PM
Location: BLOC 123
Speaker: Volodymyr Nekrashevych, Texas A&M University
Title: Conformal dimension and combinatorial modulus
Abstract: We will discuss the Ahlfors-regular conformal dimension of the limit space of a self-similar group. In particular, I will give a characterization of the conformal dimension in terms of the combinatorial modulus of the dual Moore diagram of the automaton generating the group. This is an adaptation of the characterization of the conformal dimension due to Carrasco Piaggio and Keith-Kleiner. We will also discuss a characterization of the dimension in terms of the Schatten class of commutators of natural representations of the group and the algebra of continuous functions on the limit space.