Jennifer Brown, University of Edinburgh

Title: Skein Categories in Non-semisimple Settings

Abstract:

Skein theory uses diagrammatics of braided tensor categories to build link invariants and to study moduli spaces. Many of its constructions and definitions were originally formulated for semisimple categories, but physically motivated examples are often non-semisimple. This has inspired mathematicians to update the theory to accommodate non-semisimple settings.

One of the main features in non-semisimple skein theory - admissibility conditions - is not compatible with the powerful factorization homology techniques that have found purchase in skein theory. The crux of the problem is that the tensor unit is rarely admissible, complicating many constructions.

In this talk we'll start by a introduction to skein theory, then explain the speaker's work with Benjamin Haïoun to reconcile admissibility conditions and factorization homology.