## Dynamics, Geometry, & Groups Seminar

### Friday, September 14th, 2018

**Time:** 10:30 a.m** Place:** Jeffery Hall 422

**Speaker:** Jacob Russell (CUNY)

**Title:** The geometry of groups via their boundaries

**Abstract:** Gromov revolutionized the study of finitely generated groups by purposing the study of groups as geometric objects. The success of this geometric viewpoint has inspired a whole program of classifying groups geometrically. From the geometry of the group, one can construct various boundaries; topological spaces which record the geometry of the group "at infinity". One of these boundaries, the Morse boundary, is particularly nice as the group has a natural action on it by homeomorphisms. The Morse boundary can also be equipped with a natural cross-ratio and we will discuss how the topology of the boundary coupled with this cross-ratio is actually sufficient to encode the entire geometry of the group.