Katie Haymaker, Villanova

Abstract: This talk will begin with a definition of the Cantor set, a remarkable object that enjoys many special properties. We will utilize a graph representation of the Cantor set, and focus on a group formed by a collection of maps from the graph to itself. The group is called Thompson's group V after Richard Thompson, the logician who discovered it. The goal of this talk will be to examine the group V, to study some of its unique properties, and to prove a result about the graph groups that exist as subgroups of V (Joint work with Nathan Corwin).