Date: Friday, April 12, 2013
Location: 3096 East Hall (3:00 PM to 4:00 PM)
Title: Cohomology and equidistribution for Abelian actions on nilmanifolds
Abstract: Following Katok we say that the cohomology of the action of a group $P$ on a smooth manifold $M$ is stable if the space of co-boundaries is closed in the smooth topology. A refinement of this is the notion of tame stability, a fundamental property for perturbation theory. We prove that the action of Abelian subgroups of the Heisenberg group $H^{2n+1}$ on compact quotients of $H^{2n+1}$ are tamely stable in all degrees, under a suitable Diophantine condition. As a consequence we derive precise asymptotics for the deviations of ergodic averages for these group actions. This is a work in collaboration with S.~Cosentino (University do Minho, Braga).
Speaker: Livio Flaminio
Institution: U Lille
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