## 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.

## Contact

Department of Mathematics
Michigan State University