Colloquium | Niky Kamran, Inverse scattering at fixed energy on asymptotically hyperbolic Liouville surfaces

We study an inverse scattering problem on asymptotically hyperbolic Liouville surfaces with two ends and prove that surfaces are determined uniquely (up to isometries) from the knowledge for a given fixed energy of the scattering operator for scalar waves. The main ingredients used to prove this result are the separability of the wave equation into a system of ODEs, the Complex Angular Momentum method and a reinterpretation of the partial scattering coefficients as generalized Weyl-Titchmarsh functions for a certain Sturm-Liouville equation having the complex angular momentum as spectral parameter.

This is a joint work with Thierry Daude (Cergy-Pontoise) and François Nicoleau (Nantes).