A Borg-Levinson theorem for magnetic Schrödinger operators on a Riemannian manifold

This talk is concerned with the inverse spectral problem of recovering the magnetic field and the electric potential in a Riemannian manifold from some asymptotic knowledge of the boundary spectral data of the corresponding Schrödinger operator with Dirichlet (or Neumann) boundary conditions. It combines a representation formula coming from Isozaki as well as a construction of solutions to the Schrödinger equation in simple manifolds already used by Bellassoued and myself in the quantitative study of inverse problems on the Dirichlet-to-Neumann map associated with evolution equations (also inspired by the study of the anisotropic Calderón problem by Kenig, Salo, Uhlmann and myself).

This is a joint work with Mourad Bellassoued, Mourad Choulli, Yavar Kian and Plamen Stefanov.