Orateur
Jacques Audibert
(Max Planck Institute, Leipzig)
Description
In this talk we will discuss Coxeter groups and their "Vinberg representations". These are discrete and faithful representations that are of special geometric significance. As we will show, the Zariski-closure of such representations is very restricted. This allows us to construct new examples of Zariski-dense subgroups of $\mathrm{SL}(n,\mathbb Z)$. In particular, we will prove that, for all $n$ at least $3$, $\mathrm{SL}(n,\mathbb Z)$ contains a Zariski-dense subgroup isomorphic to the fundamental group of a closed surface.
This is joint work with Sami Douba, Gye-Seon Lee and Ludovic Marquis.
