Department of Mathematics

Speaker: Kim Ruane
Title: Groups as Geometric Objects
Affiliation: Tufts University
Date: Friday, September 5, 2014
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. In this talk I will discuss how to view a finitely generated group as a geometric object via a Cayley graph. I will begin with some specific examples of some finite groups and infinite groups and the types of theorems you can prove using this viewpoint. My end goal is to discuss the group of automorphisms of a right-angled Coxeter group since very little is known about the geometry of this group. There are at least two natural generating sets for this group that one might use to study the geometry, however finding geodesics in the associated metric is a difficult problem.

I will discuss some approaches to studying these groups, some recent joint work of mine with A. Piggott and G. Walsh on particular examples of these groups, as well as some specific open questions one could try to attack about these groups.