Two spectral theories arise from the study of hyperbolic manifolds: the Laplacian, and the geodesic flow (Ruelle-Pollicott resonances). There are many results building explicit bridges between these two spectra. For Lorentzian manifolds, the elliptic Laplacian is replaced with a hyperbolic operator, leading to a completely different spectral theory. We will see that we can still connect this operator with the geodesic flow for some 3-dimensional anti-de Sitter (i.e. Lorentzian with constant negative curvature) manifolds.
Based on joint work with B. Delarue and C. Guillarmou.
