Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Commensurators and arithmeticity of hyperbolic manifolds
Speaker: Wouter van Limbeek, University of Illinois at Chicago
Date: January 24, 2022
Time: 20:00:00 Hours
Venue: via Zoom
Abstract: The commensurator of a Riemannian manifold $M$ encodes symmetries between all the finite covers of $M$, and lifts to a subgroup of isometries of the universal cover of $M$. In case $M$ is an (irreducible) finite volume locally symmetric space, the commensurator is thus a subgroup of a simple Lie group $G$. Margulis proved that if the commensurator is dense in $G$, then $M$ is arithmetic. Shalom asked if the same is true for infinite volume $M$? I will report on recent progress on this question when $M$ regularly covers a finite volume hyperbolic manifold. This is joint work with D. Fisher and M. Mj.
Title of Talk: Commensurators and arithmeticity of hyperbolic manifolds
Speaker: Wouter van Limbeek, University of Illinois at Chicago
Date: January 24, 2022
Time: 20:00:00 Hours
Venue: via Zoom
Abstract: The commensurator of a Riemannian manifold $M$ encodes symmetries between all the finite covers of $M$, and lifts to a subgroup of isometries of the universal cover of $M$. In case $M$ is an (irreducible) finite volume locally symmetric space, the commensurator is thus a subgroup of a simple Lie group $G$. Margulis proved that if the commensurator is dense in $G$, then $M$ is arithmetic. Shalom asked if the same is true for infinite volume $M$? I will report on recent progress on this question when $M$ regularly covers a finite volume hyperbolic manifold. This is joint work with D. Fisher and M. Mj.