Klaus Kröncke: Stability problems for Einstein manifolds

In this talk, I will give an overview of the stability problem for compact Einstein manifolds with respect to the Einstein Hilbert action. I will also explain how this is related to the stability problem under the Ricci flow and the nonlinear stability of some globally hyperbolic solutions of the Einstein equation in general relativity. If time permits, I will explain why the analogy to this problem in suitable noncompact settings (e.g. on ALE manifolds) is the (local) positive mass problem.