We proved that any algebraic Anosov action $\rho$ on a nilmanifold without rank-1 factor is globally rigid, i.e. any action homotopic to $\rho$ with one Anosov element is smoothly conjugated to $\rho$. This answer a question by A. Katok and R. Spatzier in the nilmanifold context. In this talk we plan to show some ideas of the proof, recall previous approaches, especially that of D. Fisher, B. Kalinin and R. Spatzier (JAMS, 2013) and discuss some related open problems. This is a joint work with Zhiren Wang.
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