Vorträge des SFB 1442

Since Hawking proved his singularity theorem, it is clear that singularities of big bang type typically occur in cosmological solutions to Einstein?s equations. Moreover, due to the work of Belinskii, Khalatnikov and Lifschitz (BKL), there is a proposal concerning the nature of these singularities. For many matter models, solutions are expected to exhibit chaotic dynamics governed by the so-called BKL map, but for some matter models, the dynamics are expected to be convergent/quiescent. The purpose of the talk is to discuss quiescent singularities, with an emphasis on a geometric notion of initial data on the singularity. In particular, we present a general condition on initial data ensuring big bang formation, curvature blow up and solutions that induce data on the singularity

In this talk, I will recall the notions of C*- and W*-superrigidity for groups. I will then present examples of non-amenable groups that can be completely reconstructed from their reduced C*-algebras, but not from their group von Neumann algebras. These groups are constructed as infinite direct sums of amalgamated free product groups and provide the first known examples of non-amenable groups exhibiting this behavior. This is joint work with Juan Felipe Ariza Mejía and Ionut Chifan.