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.