Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Metric Ergodicity and its applications in Rigidity Theory
Speaker: Uri Bader, Weizmann Institute of Science
Date: September 27, 2021
Time: 16:00:00 Hours
Venue: AG-77
Abstract: An action is called Metrically Ergodic (ME) if the acted space admits no equivariant maps to metric spaces. This is a far reaching strengthening of usual Ergodicity. For probability measure preserving actions, ME is equivalent to Weak Mixing, but in general it is different and could be thought of as a generalization of Mautner phenomenon. It is a remarkable fact that every locally compact second countable group admits an action which is both Amenable and Metrically Ergodic. For example, the celebrated fixed point theorem of Ryll-Nardzewski could be deduced easily from this fact. In another direction, it implies Super-Rigidity for Lattices in Products. It is also a main player in the proof of the Simplicity of the Lyapunov Spectra in various situations. In my talk I will provide a gentle introduction to ME and discuss its applications.
Title of Talk: Metric Ergodicity and its applications in Rigidity Theory
Speaker: Uri Bader, Weizmann Institute of Science
Date: September 27, 2021
Time: 16:00:00 Hours
Venue: AG-77
Abstract: An action is called Metrically Ergodic (ME) if the acted space admits no equivariant maps to metric spaces. This is a far reaching strengthening of usual Ergodicity. For probability measure preserving actions, ME is equivalent to Weak Mixing, but in general it is different and could be thought of as a generalization of Mautner phenomenon. It is a remarkable fact that every locally compact second countable group admits an action which is both Amenable and Metrically Ergodic. For example, the celebrated fixed point theorem of Ryll-Nardzewski could be deduced easily from this fact. In another direction, it implies Super-Rigidity for Lattices in Products. It is also a main player in the proof of the Simplicity of the Lyapunov Spectra in various situations. In my talk I will provide a gentle introduction to ME and discuss its applications.
The talk is based on a joint work with Alex Furman.