Department of Mathematics

Dynamical Systems

  •  Zhenqi Wang, Michigan State University
  •  Local rigidity of higher rank partially hyperbolic algebraic actions
  •  11/01/2022
  •  3:00 PM - 4:00 PM
  •  A136 Wells Hall
  •  Huyi Hu (hhu@msu.edu)

We give a complete solution to the local classification program of higher rank partially hyperbolic algebraic actions. We show $C^\infty$ local rigidity of abelian ergodic algebraic actions for symmetric space examples, twisted symmetric space examples and automorphisms on nilmanifolds. The method is a combination of representation theory, harmonic analysis and a KAM iteration. A striking feature of the method is no specific information from representation theory is needed. It is the first time local rigidity for non-accessible partially hyperbolic actions has ever been obtained other than torus examples. Even for Anosov actions, our results are new: it is the first time twisted spaces with non-abelian nilradical have been treated in the literature.

 

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Michigan State University
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