Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## On twisted translation flows

Prof. Dr. Giovanni Forni talk

Speaker invited by: Prof. Dr. Corinna Ulcigrai

**Date:** 15.10.18 **Time:** 15.30 - 16.30 **Room:** Y27H25

We study cohomological equations and ergodic integrals for twisted translation flows, define as products of a translation flow on a translation surface and a linear flow on a circle. By standard Fourier analysis the questions we consider reduce respectively to non-homogeneous cohomology equations with purely imaginary constant zero-order term (twisted cohomological equation) and to ergodic integrals of functions times an exponential of time with purely imaginary phase (twisted ergodic integrals). The motivation is two-fold: on the one hand we want to understand a simple example of 3-dimensional translation flow, on the other hand there is a well-known close connection between twisted ergodic integrals and spectral measures of translation flows, already exploited in the work of Bufetov-Solomyak. In this respect our aim is to cast their work in more geometric terms and to generalize it.