Two results on rigidity of commutative actions by toral automorphisms

Two results on rigidity of commutative actions by toral automorphisms

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Zhiren Wang, Princeton University
Fine Hall 401

In 1983 Berend proved rigidity of higher-rank commutative actions by toral automorphisms under some hyperbolicity and irreduciblity assumptions. We will present two rigidity results that respectively extend Berend's theorem to certain non-hyperbolic and reducible cases. We will also discuss some counterexamples of non-homogeneous orbit closures. This is joint work with Elon Lindenstrauss.