Topological and Conformal Dimensions of Self-Similar Groups

Explore the intricate relationship between self-similar contracting groups and their limit dynamical systems in this 50-minute conference talk from the Workshop on "Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the concept of limit spaces as compact topological spaces associated with locally expanding maps, and understand how these groups function as iterated monodromy groups of their limit dynamical systems. Examine the connections between the algebraic properties of self-similar groups and the geometric characteristics of their limit spaces, with a particular focus on the algebraic aspects of topological and conformal dimensions. Gain insights into this complex area of mathematics through the expertise of Volodymyr Nekrashevych, expanding your understanding of geometric and asymptotic group theory.