Geometry, Topology and Dynamics Seminar
Boris Kalinin
Penn State University
Global smooth rigidity for Anosov Z^k actions on tori and nilmanifolds.
Abstract: Any smooth action of Z^k on a torus or nilmanifold with a hyperbolic
element is topologically conjugate to a Z^k action by commuting
affine automorphisms. It is conjectured that the conjugacy is in fact
smooth provided that the action is genuinely higher rank. I will give
an overview of this area and present my recent work with D. Fisher and
R. Spatzier in which we prove this conjecture for actions with sufficiently
many hyperbolic elements. We use a new approach which employs exponential
decay of correlations and harmonic analysis. In particular, we establish
a regularity result for functions whose derivatives along several transverse
foliations exist as distributions on Holder functions.
Monday March 4, 2013 at 3:00 PM in SEO 636