Anosov Representations and Spectral Theory

In this talk I want to report on recent advances on spectral theory for Anosov representations. Motivated by the theory of Laplace and Ruelle resonances for convex cocompact hyperbolic surfaces I will discuss the corresponding higher rank analogs, i.e. the joint spectrum of the Algebra of invariant differential operators and Weyl chamber flows. In particular I want to explain how the spectral theoretic results imply new results for the Anosov subgroups, such as bounds on growth rates of meromorphic Poincaré series.