# Boris Kalinin: Smooth local rigidity for hyperbolic toral automorphisms

**Time: **
Thu 2021-10-14 15.00 - 16.00

**Location: **
Zoom meeting ID: https://kth-se.zoom.us/j/61173989405

**Lecturer: **
Boris Kalinin (Penn State)

**Abstract: **This is a joint work with Victoria Sadovskaya and Zhenqi Jenny Wang. We study the regularity of a conjugacy H between a hyperbolic toral automorphism A and its perturbation f. We show that if H is weakly differentiable (for example Lipschitz) then it is C^{1+Holder} and, if A is also weakly irreducible, then H is C^\infty. As a part of the proof we establish results of independent interest on Holder continuity of a measurable conjugacy between linear cocycles over a hyperbolic system. As a corollary, we improve regularity of the conjugacy to C^\infty in prior local rigidity results.