Weak mixing for interval exchange transformations and translation flows

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 2 (with prescribed singularity types) is weakly mixing. *A. Avila would like to thank Jean-Christophe Yoccoz for several very productive discussions and Jean-Paul Thouvenot for proposing the problem and for his continuous