## Dynamics, Geometry, & Groups - Catherine Pfaff (Queen's University)

### Wednesday, May 15th, 2019

**Time:** 2:00 p.m** Place:** Jeffery Hall 319

**Speaker:** Catherine Pfaff (Queen's University)

**Title:** Counting Conjugacy Classes: Groups Rebelling Against Dynamics.

**Abstract:** This talk will start with a gentle introduction to ways of viewing outer automorphisms of free groups and then will discuss joint work with Ilya Kapovich regarding counting conjugacy classes of these outer automorphisms. That is, inspired by results of Eskin and Mirzakhani counting closed geodesics of bounded length in the moduli space of a fixed closed surface, we consider a similar question in the Out(F_r) setting and discover bounds revealing behavior not present in the surface setting or in classical hyperbolic dynamical systems.