Title: Groups, Graphs and Trees
Abstract: What do we mean by the geometry of a group? Groups seem like very abstract objects when we first study them, and it’s natural to ask whether we can visualize them in some way. Given a group with a finite set of generators and relators, I will describe a canonical way to construct a geometric model of that group, called a Cayley graph. We will see many examples — both standard and unusual — and I will discuss some fundamental questions from the field of geometric group theory, including whether this geometric model is well defined. One goal of this field of mathematics is to use the geometry of a group to provide insight into its algebraic structure, and to use the algebraic properties of a group to draw conclusions about its geometry. This will be a very visual talk, involving many examples of groups, graphs, and trees.
Dr. Jennifer Taback is Isaac Henry Wing Professor and Chair of the Mathematics Department at Bowdoin College.