Gabriel Paternain (Cambridge)

Spectral rigidity and invariant distributions on Anosov surfaces

Abstract: I will discuss inverse problems on a closed Riemannian surface whose geodesic flow is Anosov. More specifically, I will try to establish spectral rigidity for a class of Anosov surfaces that may have focal points and surjectivity results for the adjoint of the geodesic ray transform on tensors. These surjectivity results imply the existence of many geometric distributions in H^{-1} invariant under the geodesic flow. This is joint work with Mikko Salo and Gunther Uhlmann.