## Groups and Dynamics Seminar

**Date: ** November 1, 2023

**Time: ** 3:00PM - 4:00PM

**Location: ** BLOC 628

**Speaker: **Volodymyr Nekrashevych, Texas A&M University

**Title: ***Locally connected Smale spaces*

**Abstract: **We will discuss Ruelle-Smale dynamical systems (hyperbolic topological dynamical systems), a.k.a. Smale spaces. They are topological generalizations of Anosov diffeomorphisms. One of the main open questions is characterization of the algebraic Ruelle-Smale spaces (i.e., covered by hyperbolic automorphisms of nilpotent Lie groups) in purely topological terms. For example, no non-algebraic examples of locally connected Smale spaces are known. We will discuss known results about this problem and its connection to group theory.