Abstract: 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 SL(n,Z). In particular, we will prove that, for all n at least 3, SL(n,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.
If you are interested in participating online please contact Tobias Weich or Benjamin Delarue in order to receive the login details.