Topological mixing for some residual sets of interval exchange transformations

Abstract: We show that a residual set of non-degenerate IETs on more than 3 letters is topologically mixing. This shows that there exists a uniquely ergodic topologically mixing IET. This is then applied to show that some billiard flows in a fixed direction in an L-shaped polygon are topologically mixing. This is joint work with Jon Chaika.