Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Discrete stationary random subgroups and application to discrete subgroups of Lie groups
Speaker: Tsachik Gelander, Weizmann Institute of Science
Date: September 20, 2021
Time: 16:00:00 Hours
Venue: AG-77
Abstract: The notion of invariant random subgroups (IRS) has proven extremely useful during the last decade, particularly to the study of asymptotic invariants of lattices. However, the scope of problems that one can investigate when restricting to invariant measures (on the space of subgroups)is limited. It was recently realised that the notion of stationary random subgroups (SRS), which is much more general, is still extremely powerful and opens up new paths to attacking problems that previously seemed to be out of our reach.
Title of Talk: Discrete stationary random subgroups and application to discrete subgroups of Lie groups
Speaker: Tsachik Gelander, Weizmann Institute of Science
Date: September 20, 2021
Time: 16:00:00 Hours
Venue: AG-77
Abstract: The notion of invariant random subgroups (IRS) has proven extremely useful during the last decade, particularly to the study of asymptotic invariants of lattices. However, the scope of problems that one can investigate when restricting to invariant measures (on the space of subgroups)is limited. It was recently realised that the notion of stationary random subgroups (SRS), which is much more general, is still extremely powerful and opens up new paths to attacking problems that previously seemed to be out of our reach.
In this talk, using the notion of SRS, I will explain a proof of the following conjecture of Margulis: Let $G$ be a higher rank simple Lie group and $\Lambda \subset G$ a discrete subgroup. Then the orbifold $\Lambda \setminus G/K$ has finite volume if and only if it has bounded injectivity radius. This is a far-reaching generalisation of the celebrated Normal Subgroup Theorem of Margulis, and while it is new even for subgroups of lattices, it is completely general.
This is a joint work with Mikolaj Fraczyk.