Palazzo della Carovana, Aula Russo.
Amenable groups are small from a large-scale geometric point of view. If a space can be covered by a few subsets with an amenable fundamental group, there are strong vanishing results for several invariants: simplicial volume, $L^2$-Betti numbers, and homology growth. We study the minimal number of such subsets needed to cover a space, the so-called amenable category. In the talk, we focus on aspherical spaces and compute this number for right-angled Artin groups.