# Weak mixing for interval exchange transformations and translation flows

### Abstract

We prove that a typical interval exchange transformation is either weakly mixing or it is an irrational rotation. We also conclude that a typical translation flow on a typical translation surface of genus $g \geq 2$ (with prescribed singularity types) is weakly mixing.

## Authors

Artur Ávila

CNRS UMR 7599, Université Pierre et Marie Curie, 75252 Paris, France

Giovanni Forni

Department of Mathematics, University of Toronto, Toronto, ON, Canada M5S 2E4