Topological and measurable full groups
WiSe 2024/25
Organizers: Shirly Geffen, David Kerr, Ola Kwiatkowska, Katrin Tent
Coordinates: Mondays 10:00–12:00 in SR1D

Actions of a countable group on the Cantor set or a standard measure space naturally give rise to larger groups of transformations of the space which act piecewise via elements of the original acting group. These “full groups” come with a Polish topology which may be discrete (in the topological setting) or non-locally-compact (in the measure-theoretic setting). They are closely related to both orbit equivalence theory and operator algebras and have revealed themselves over the last fifteen years to be a rich source of novel phenomena at the abstract group-theoretic level.

This introductory seminar will treat both topological and measurable full groups, with an eye towards properties such as simplicity, finite generation, amenability, and nonamenability and their relation to the underlying dynamics.

Schedule
1 — Oct 14, Topological full groups: basics, Ola Kwiatkowska
2 — Oct 21, Topological full groups: simplicity, Silke Meißner
3 — Oct 28, Topological full groups: finite generation, Hannah Boß
4 — Nov 4, Topological full groups: homology, Nils Pokorny
5 — Nov 18, Juschenko-Monod theorem I, Marco Amelio
6 — Nov 25, Juschenko-Monod theorem II, Dan Ursu
7 — Dec 2, L1 full groups I, Anna Cascioli
8 — Dec 9, L1 full groups II, Grigoris Kopsacheilis
9 — Dec 16, L1 full groups III, Spyros Petrakos
10 — Jan 13, L1 full groups IV (nonamenability), Shirly Geffen
11 — Jan 20, Topological full groups: nonamenability I, Katrin Tent
12 — Jan 27, Topological full groups: nonamenability II, Robin Sroka