Weingarten Calculus is a tool to compute integrals of polynomial functions over compact groups with respect to their probability Haar measure (or equivalently, the expectation of polynomial variables). While the existence of Haar measure has been known for almost 100 years in a non-constructive way, an effective method to compute integrals or expectations started being investigated systematically only about 50 years ago (by the Nobel Prize winner ’t Hooft, Weingarten, and other theoretical physicists). The mathematical aspects of this theory are much more recent, and we will review them as well as some of our contributions to the field. In particular, we will describe new methods to compute integrals over unitary groups using the notion of virtual isometries. This latter part is joint work with Sho Matsumoto (Kagoshima University).

15:10-16:10 Talk by Prof. Narutaka Ozawa
16:10-16:45 Tea Break
16:45-17:45 Talk by Prof. Neal Bez