Description:

Title: Magnetic Marked Length Spectrum Rigidity

Abstract: Given a closed Riemannian manifold with everywhere negative sectional curvature, there exists a unique geodesic inside of every non-trivial free homotopy class. The marked length spectrum is defined to be the function which takes a free homotopy class and returns the length of this geodesic. It was conjectured by Burns and Katok that the marked length spectrum determines a Riemannian metric up to isometry. In this talk, I'll present the "magnetized" version of this conjecture and discuss recent progress showing that for certain magnetic flows on surfaces, the periods of closed orbits still encode the underlying geometry. This is joint work with Valeria Assenza, Jacopo de Simoi, and Ivo Terek.