| Résume | If vanishing of a countable family of invariants implies a strong form of equivalence, then one speaks about rank one rigidity. There has been lots of progress on local rigidity in various settings when one additionally assumes that dynamical systems are close to each other. Making such results global is usually a challenging problem. I will discuss recent progress on global rigidity in the setting of higher dimensional Anosov diffeomorphisms. Based on joint works with Jonathan DeWitt and with Federico Rodriguez Hertz. |