Speaker: Phillip Wesolek (Weslyan U.)
Title: An invitation to totally disconnected locally compact groups
Abstract: Locally compact groups appear across mathematics; they arise as Galois groups in algebra, isometry groups in geometry, and full groups in dynamics. The study of locally compact groups splits into two cases: the connected groups and the totally disconnected groups. There is a rich and deep theory for the connected groups, which was developed over the last century. On the other hand, the study of the totally disconnected groups only seriously began in the last 30 years, and moreover, these groups today appear to admit an equally rich and deep theory. In this talk, we will begin by motivating the study of totally disconnected locally compact groups and presenting several examples. We will then discuss a natural dividing line in the theory and a fundamental decomposition theorem.