# Meeting Details

Title: Cohomological equation, invariant distributions and quantitative unique ergodicity for Heisenberg nilflows. Working Seminar: Dynamics and its Working Tools Giovanni Forni, University of Maryland This is the third lecture form the DISTINGUISHED VISITING PROFESSOR LECTURE SERIES INVARIANT DISTRIBUTIONS AND RENORMALIZATION IN PARABOLIC DYNAMICS.'' ======================================================== Abstract: In this lecture we describe joint work with L. Flaminio on how to use the theory of unitary representations to construct solutions of the cohomological equation for Heisenberg nilflows and how to apply that result to precise bounds on the speed of convergence of ergodic averages. Such bounds are related to bounds on the so-called Weyl sums (already known by methods of analytic number theory). The approach is exactly the same as for the horocycle flow, discussed in Lecture 1. The main difference is the appearance of a renormalization dynamics on a 'moduli space' of Heisenberg nilmanifold.