# Meeting Details

Title: Cohomological equation, invariant distributions and quantitative unique ergodicity for horocycle flows. Working Seminar: Dynamics and its Working Tools Giovanni Forni, University of Maryland This is the first lecture form the DISTINGUISHED VISITING PROFESSOR LECTURE SERIES INVARIANT DISTRIBUTIONS AND RENORMALIZATION IN PARABOLIC DYNAMICS.'' ============================================= In this lecture we describe our joint work with L. Flaminio on how to use the theory of unitary representations to construct solutions of the cohomological equation for horocycle flows and how to apply that result to obtain precise bounds on the speed of convergence of ergodic averages. The key idea (related towork on decay of correlations for Anosov flows by Blank-Keller-Liverani, Liverani-Gouezel, Baladi-Tsuji, ... ) is to study the action of a `renormalization' dynamics, in this case the geodesic flow, on the space of invariant distributions for the horocycle flow.