Alejandra Garrido (Universidad Complutense de Madrid, ICMAT)

Title:
Simple totally disconnected locally compact groups

Abstract:
Since the start of the century there has been increased interest in totally disconnected locally compact (tdlc) groups and a structure theory is starting to emerge. A special role is played by the class S of tdlc groups that are compactly generated, topologically simple and not discrete. The theory is in need of more examples with a view to some sort of classification.

Full groups of homeomorphisms of the Cantor space are a rich source of simple groups. In joint work with Colin Reid, it is shown that, given the right conditions on the "seed" group, the full group can be given a totally disconnected locally compact topology and it contains a big simple compactly generated subgroup. An example of this is Neretin's group of almost automorphisms of a tree, further examples will be given.

It is also shown that this construction accounts for all groups in one of the five types of groups in S, up to local isomorphism (the totally disconnected analogue of having the same Lie algebra in the connected case).

No knowledge of topological groups will be assumed for this talk. 

Schedule:
09:30-11:00 RTG Lecture 1 (Matteo Migliorini), SR. 2.058
11:00-11:30 Get-Together with Speaker, SR. 1.058
11:45-12:45 Colloquium, SR. 1.067
13:15 Lunch at Max Rubner Institute | Daily Menu
14:30 Coffee in math building, SR. 1.058
14:45-15:15 Informal meeting of PhD students, Room 1.062
15:15-16:45 RTG Lecture 2 (Florent Schaffhauser), SR. 1.067

KA