On mixing rates for time-changes of Heisenberg Nilflows

(joint work with A. Kanigowski)

We construct ''Bufetov functionals'' for nilpotent flows on (compact) Heisenberg nilmanifolds. Such functionals were first constructed by Bufetov for Interval Exchange Transformations and Translation flows, and later for horocycle flows by Bufetov and myself. The main applications are (stretched) polynomial mixing rates for nontrivial time changes (improving on a result by Avila, Ulcigrai and myself that such flows are mixing), and limit theorems for Heisenberg nilflows (extending in part results of Griffin and Marklof and Cellarosi and Marklof on the related question of limit distributions of theta sums).