Totally disconnected, locally compact groups
by George Willis
Abstract: Locally compact groups occur in many branches of mathematics. Their study falls into two cases: connected groups, which occur as automorphisms of smooth structures such as spheres for example; and totally disconnected groups, which occur as automorphisms of discrete structures such as trees. The talk will give an overview of the currently developing structure theory of totally disconnected locally compact groups.
Techniques for analysing totally disconnected groups will be described that correspond to the familiar Lie group methods used to treat connected groups. These techniques have played an essential role in the solution of problems from diverse areas of mathematics and are contributing to the investigation of simple totally disconnected groups.