Alessandro Carderi: Asymptotic invariants of lattices in locally compact groups
The aim of our work is to understand some of the asymptotic properties of sequences of lattices in a fixed locally compact group. As an example we are interested in the asymptotic growth of the Betti numbers of the lattices renormalized by the covolume or the rank-gradient, the minimal number of generators also renormalized by the covolume. For doing so we will consider the ultraproduct of the actions of the locally compact group on the coset spaces and we will show how the properties of one of its cross sections are related to the asymptotic properties of the lattices.
