I will review some old and new theorems on orbit closures and classification of invariant measures. We will start with the homogeneous space setting where the theory is most mature. We will then survey some recent developments outside of the homogeneous setting. 

Upper bound on the number of resonances for even asymptotically hyperbolic manifolds real-analytic at infinity.
Abstract I will explain how tools of real-analytic microlocal analysis can be used to prove a polynomial upper bound on the number of resonances for an asymptotically hyperbolic manifold with real-analytic ends (after recalling the definition of those). The proof is based on an adaptation of Vasy’s method, introducing an analytic Fourier-Bros-Iagolnitzer transform in the spirit of the work of Helffer and Sjöstrand.This strategy has similarities with my previous work with Yannick Bonthonneau on real-analytic Anosov flows, and also gives a bound on the number of quasi-normal frequencies for Schwarzschild-de Sitter black holes.

A relaxed-pace seminar on impromptu subjects related to the interests of the audience.

Everyone is welcome.

The subjects are geometry, probability, combinatorics, dynamics, and more!