George Willis, Pierre-Emmanuel Caprace - A Totally Disconnected Invitation to Locally Compact Groups

Explore the fascinating world of topological groups that are locally compact and totally disconnected in this 45-minute lecture by George Willis and Pierre-Emmanuel Caprace. Delve into the various manifestations of these groups, including Lie groups over local fields, Kac-Moody groups, Galois groups of field extensions, and automorphism groups of locally finite graphs. Discover recent advancements in the general theory, focusing on the significance of simple groups, local structure, and comparisons with linear groups. Examine the interplay between algebra and topology, as well as the dynamics of the conjugation action. Learn about structure theory, decomposition theory, essentially chief series, and simple tdle groups. Investigate automorphisms, tidy subgroups, and their dynamics, along with contraction groups and the scale. Explore applications to random walks and ergodicity, flat groups of automorphisms, and criteria for groups of automorphisms to be flat. Access accompanying slides for visual support throughout this comprehensive exploration of locally compact groups.

Intro
Structure theory of locally compact groups
Totally disconnected locally compact groups
Decomposition theory
Essentially chief series
Simple groups
Simple tdle groups
Automorphisms of tdle groups and their scale
Minimising subgroups are tidy and conversely
Tidy subgroups and dynamics
Contraction groups and the scale
Applications to random walks and to ergoxicity
Flat groups of automorphisms
Criteria for groups of automorphisms to be flat