Pierre-Emmanuel Caprace, Université catholique de Louvain
Totally disconnected, locally compact groups (local structure)

George Willis, University of Newcastle
Totally disconnected, locally compact groups (the scale and minimising subgroups)

Lewis Bowen, Texas A & M University
Sofic groups

Helge Glöckner, University of Paderborn (Germany)
Expansive automorphisms of totally disconnected, locally compact groups (slides)

An automorphism f of a totally disconnected, locally compact group G is called expansive if there exists an identity neighborhood V in G for which the sets f^n(V) (for n ranging through the set of integers) intersect in the trivial group {1}. For example, every contractive automorphism (i.e., f^n(x) converges to 1 as n tends to infinity, for each x in G) is expansive. The structure of expansive automorphisms of pro-finite groups was elucidated by G.A. Willis (who called them "automorphisms of finite depth"). In the talk, I'll explain recent results concerning expansive automorphisms for general, not necessarily compact groups, obtained in joint work with C.R.E. Raja (see arXiv:1312.5875).

Phillip Wesolek, University of Illinois
Constructible totally disconnected locally compact second countable groups and applications (slides)

The class of constructible totally disconnected locally compact second countable (t.d.l.c.s.c.) groups is the collection of t.d.l.c.s.c. groups built from profinite and discrete groups via group extension and countable increasing union. These groups appear often in the study of t.d.l.c.s.c. groups. We show this class satisfies surprisingly robust closure properties. We go on to give an application to the study of ${p}$-adic Lie groups. In particular, we show every ${p}$-adic Lie group decomposes into constructible and topologically simple groups via group extensions. This result is analogous to the solvable by semi-simple decomposition for connected Lie groups. Time permitting, we discuss a second application to a question of S. Gao's on surjectively universal t.d.l.c.s.c. groups.

A locally compact group is said to be distal if under the conjugacy action of the group on itself, the orbit of every non-trivial element stays away from the identity. We study properties of distal groups and characterise (pointwise) distal groups in terms of behaviour of convolution powers of probability measures. (Most of the results are obtained jointly with C.R.E. Raja).