Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

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.