# Groups & Dynamics seminar Arie Levit (Yale): Critical exponents of invariant random subgroups in negative curvature

Title : "Critical exponents of invariant random subgroups in negative curvature"
Abstract : "I will talk about the critical exponent associated to an invariant random subgroup of a rank one simple Lie group G. We show that this critical exponent is greater than 1/2(dim(G/K)-1), and moreover the critical exponent is precisely dim(G/K)-1 if the IRS is almost surely of divergence type. This can be viewed as a generalization of Kesten's theorem for IRS in G. Whenever G has Kazhdan's property (T) it follows that an ergodic IRS of divergence type is a lattice. Most of our results hold true more generally for IRS in the isometry group of any Gromov hyperbolic metric space.
This is a joint work with Ilya Gehktman."

## Date:

Thu, 07/06/2018 - 10:30 to 12:00