Dynamics Seminar: Asaf Katz (Chicago): "Quantitative disjointness of nilflows and horospherical flows."

Tue, 19/12/201714:15-15:15
Ross 70
In his influential disjointness paper, H. Furstenberg proved that weakly-mixing systems are disjoint from irrational rotations (and in general, Kronecker systems), a result that inspired much of the modern
research in dynamics. Recently, A. Venkatesh managed to prove a quantitative version of this
disjointness theorem for the case of the horocyclic flow on a compact Riemann surface.
I will discuss Venkatesh's disjointness result and present a generalization of this result to more general actions of nilpotent groups, utilizing structural results about nilflows proven by Green-Tao-Ziegler.
If time permits, I will discuss certain applications of such theorems in sparse equidistribution problems and number theory.