Abstract:
Recently, there has been much progress made in understanding mechanisms for
mixing in hyperbolic flows that preserve a contact structure, starting with
contact Anosov flows and recently extended to finite horizon dispersing
billiards.  This pair of lectures will present an introduction to the main
ideas used in these proofs, focusing on the simpler Anosov case.  The first
lecture will focus on framing the question and the functional analytic
setup used to answer it.  The second lecture will present the delicate
cancellation estimate needed to complete the argument, which relies on the
contact form.