Title: Fundamental groups of asymptotic cones
Abstract: An asymptotic cone of a group is a metric space associated to a group which encodes the large scale geometry of the group. Gromov was first to notice a connection between the topology of an asymptotic cone of a group and the algorithmic properties of the group. I will explore the relationship between the topological structure of an asymptotic cone and the algebraic structure of the underling group. As well, I will discuss several techniques for studying the fundamental group of an asymptotic cone. This is joint with Greg Conner and Mark Sapir.