Strong ergodicity versus spectral gap for group actions on measure spaces
Event details
| Date | 24.05.2018 |
| Hour | 13:00 › 14:00 |
| Speaker | Cyril Houdayer (Université de Paris-Sud) |
| Location | |
| Category | Conferences - Seminars |
It is well-known that for probability measure preserving (pmp) group actions, if the associated Koopman representation has spectral gap (i.e. has no almost invariant vectors), then the action is strongly ergodic (i.e. has no non-trivial almost invariant measurable subsets). The converse is however not true as demonstrated by Schmidt’s example.
In this talk, I will present a characterization of strong ergodicity for arbitrary nonsingular group actions in terms of a spectral gap property of the full group of the associated orbit equivalence relation. I will then explain how this criterion can be used to characterize strong ergodicity of the Maharam extension of group actions of type III in terms of a new invariant, analogous to Connes tau invariant for von Neumann type III factors. This is joint work with A. Marrakchi and P. Verraedt.
Practical information
- Informed public
- Free