Makoto Yamashita (from Ochanomizu University in Tokyo)
Title: Harmonic analysis on monodical categories
Abstract: Monodical categories, or tensor categories appear in many branches of mathematics and mathematical physics, as powerful framework to capture symmetry of various structures. In this lecture I give a review of recent developments on harmonic analytic aspects of tensor categories. This unifies Popa's work on approximation properties for standard invariants  of subfactors, and the functional analytic study of quantum groups, both motivated by the noncommutative harmonic analysis, while allowing us to bring in interesting ideas from quantum field theory. Casting the famous Drinfeld-Jimbo q-deformation quantum groups in this context, we obtain a rich analogy with classical unitary representation theory of complex semisimple Lie groups.