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.