[Topology and Geometry Seminar] "Solving Word Problems in finitely presented groups" by Robert Tang

A standard way to define an abstract group is via a presentation; this amounts to writing down some generators and relations. One of the fundamental problems for finitely presented groups is the Word Problem, first posed by Dehn: find an an algorithm that can decide whether two given words (or products) using the generators represent the same group element. We will discuss geometric approaches to solving the Word Problem using Cayley Graphs and ideas from hyperbolic geometry.