# Meeting Details

Title: Global rigidity of abelian Anosov actions on tori Center for Dynamics and Geometry Seminars Zhiren Wang, Yale University As part of a more general conjecture by A. Katok and R. Spatzier, the following statement was expected to hold: if a smooth $\mathbb Z^r$-action $\alpha$ on a torus contains one Anosov element and has no rank-1 factor, then it must be smoothly conjugate to its linearization $\alpha_0$, which is an action by toral automorphisms. D. Fisher, B. Kalinin and R. Spatzier showed this holds under the assumption that $\alpha$ has at least one Anosov element in every Weyl chamber of the linearization action. We will verify that this assumption is redundant, hence fully establish the statement above. This is a joint work with Federico Rodriguez Hertz.