The marked length spectrum of Anosov manifolds

We show some new rigidity result for the marked length spectrum of closed negatively curved manifolds (and more generally those with Anosov geodesic flows) in any dimension, answering partially a conjecture of Burns-Katok in ’85. The marked length spectrum is the length of closed geodesics, ordered by their free homotopy classes. This is joint work with T. Lefeuvre.