Rigidity results in Riemannian geometry, the case of geodesic lengths

I will survey some recent results on the boundary rigidity problem and the marketed  length spectrum rigidity in negative curvature (Anosov case) and explain how analytic methods manage to make progress on these problems.

You can learn more about Professor Colin Guillarmou at https://www.imo.universite-paris-saclay.fr/~guillarmou/