Andrey Gogolev ( Ohio State University)

Title: Rigidity - From geometry to Dynamics and back

Abstract

Celebrated Otal-Croke marked length spectrum rigidity theorem recovers the geometry of a closed negatively curved surface from discrete data: the periods of closed geodesics on the surface. As an intermediate step of the proof the dynamics of the (Anosov) geodesic flow is recovered from the periods. We generalize this dynamical rigidity result to the setting of volume preserving 3-dimensional Anosov flows. In turn, it leads to a more general “weighted” marked length spectrum rigidity for negatively curved surfaces. Joint work with F. Rodriguez Hertz.