Almost every 3-IET is not simple

This talk will present that almost every 3-IET is not simple.
That is, it has ergodic self joinings that are neither the product measure
nor "supported on a graph." This answers a question of Veech. Moreover, the
ergodic self joinings are (weak-*) dense in the self-joinings. Relevant
terminology will be defined. This is joint work with Alex Eskin.