Let G be a simple higher rank Lie group and let X be the associated symmetric space. Margulis conjectured that any discrete subgroup \Gamma of G such that X/\Gamma has uniformly bounded injectivity radius must be a lattice. I will present the proof of this conjecture and explain how stationary random subgroups play the central role in the argument. The talk is be based on a recent joint work with Tsachik Gelander.

Zoom link: https://iu.zoom.us/j/661711533?pwd=RTFVTjMrQ1pYTCtIZzIvVGVvODV2QT09
password is 076877 if needed. Speaker(s): Mikolaj Fraczyk (The University of Chicago)