June 4 | Kevin Walker (Microsoft Quantum)
3-categorical group actions and 2d SET models
There is a general procedure for constructing an n-dimensional symmetry-enhanced topological phase (SET) model from an (n+1)-categorical group action. After warming up with the n=1 case of this construction, I'll spend most of the talk on the n=2 case. Hopefully there will also be time to briefly discuss the n=3 case. One of the key points is making a sufficiently general definition of "(n+1)-categorical group action". I'll present a definition which goes beyond what's usually found in the tensor category literature. My hope is that this will be a fairly informal talk with plenty of back-and-forth with the audience.
April 30 | Wade Bloomquist (UCSB)
May 28 | Vijay Higgins (UCSB)
Combinatorial Approaches to Webs and Foams
In 1999, Khovanov categorified the Jones polynomial by associating a chain complex to each link diagram. This sl_2 construction has since been generalized to the sl_n case. A helpful ingredient in these constructions is the categorification of planar webs by foams. I will present Robert and Wagner's 2017 combinatorial sl_n foam evaluation formula and explain how they use it to categorify sl_n webs. We hope that these ideas can be applied outside of type A.