Georgia Institute of Technology College of Sciences

A starting point of geometric group theory is thinking of a group as a geometric object, by giving it a metric induced from the Cayley graph of the group. Gromov initiated a program of studying groups up to quasi-isometries, which are ``bilipschitz maps up to bounded additive error". Quasi-isometries ignore local structure and preserve asymptotic properties of a metric space. In the talk I will give a sample of results, examples, and open questions in this area.