Dominik Gruber

Gromov's monsters are finitely generated groups whose Cayley graphs contain expander graphs in a reasonable geometric sense - a property of great interest in geometric and analytic group theory.

I will discuss the two known constructions of such groups and explain that they yield two classes of groups that are very different with respect to their actions on and geometric features of Gromov hyperbolic spaces.

Based on joint works with Alessandro Sisto and Romain Tessera