Abstract:

Fusion categories are generalizations of the representation categories of finite groups. One source of new fusion categories are subfactors, inlusions of von Neumann algebras with trivial center. The search for exotic subfactors led to new interesting fusion categories. One can study chiral conformal field theory via so-called conformal nets. I will explain how conformal nets give rise to fusion categories via its (higher) representation theory. It is an open question if all unitary fusion categories come from conformal nets. I will give examples of families of fusion categories for which one can reconstruct a conformal net.

Time: Wed., 4pm; Room: APM 6402 (Please notice the unusual time, day, and location.)

  Abstract:

I will describe an ongoing project to study slices to Schubert varieties in the affine Grassmannian. These are Poisson varieties, and we will be mainly interested in quantizing them. The resulting algebras, called truncated shifted Yangians, have a beautiful representation theory. We will discuss this and also mention some connections to Nakajima quiver varieties which were recently discovered by Braverman-Finkelberg-Nakajima and Webster. In the pre-talk I'll define the affine Grassmannian and discuss its role in geometric representation theory.

  Abstract:

We give a survey on recent work of Bao, Chan, Gaddis, He, Kirkman, Moore, Walton, Won, and others in noncommutative invariant theory.

Room: APM 5402 (Please notice the unusual location.)