# 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