# Meeting Details

Title: Quantitative ergodicity for some nilflows on higher step nilmanifolds Working Seminar: Dynamics and its Working Tools Giovanni Forni, University of Maryland This is the fourth lecture form the DISTINGUISHED VISITING PROFESSOR LECTURE SERIES INVARIANT DISTRIBUTIONS AND RENORMALIZATION IN PARABOLIC DYNAMICS.'' ======================================================== We describe joint work with L. Flaminio which addresses the problem of quantitative ergodicity in one case where no 'natural' renormalization dynamics seem to exist. We argue that 'renormaization' , that is a full-fledged hyperbolic dynamical system exhibiting non-trivial recurrence, can be replaced by a rescaling with trivial, non-recurrent dynamics as long as one is able to control the escape rate of points in a 'deformation' space. We conclude by surveying related results, open questions and directions for future research.