# Talk

Modul:   MAT760  Ergodic Theory and Dynamical Systems Seminar

## Resonances of Nilmanifold Automorphisms and Properties of Nilflows

Dr. Lucia Dora Simonelli talk

Speaker invited by: Prof. Dr. Corinna Ulcigrai

Date: 12.11.18  Time: 15.30 - 16.30  Room: Y27H25

We start by considering the Heisenberg nilflow renormalized by a partially hyperbolic automorphism of the nilmanifold. Through this renormalization, we show that the spectrum of the transfer operator of the partially hyperbolic map gives information about the (parabolic) nilflow - in particular, information about deviation of ergodic averages and regularity of the cohomological equation. Then we discuss the spectral information of more general partially hyperbolic systems and their relationship to a larger class of parabolic flows. (Joint work with Oliver Butterley.)