  We show that every transformation is disjoint from almost every interval
exchange transformation (IET), answering a question of Bufetov. In particular,
we prove that almost every pair of IETs is disjoint. It follows that the
product of almost every pair is uniquely ergodic. A key step in the proof is
showing that any sequence of density 1 contains a rigidity sequence for almost
every IET, strengthening a result of Veech.
