Two field theories can sometimes meet at a codimension one defect, which carries the information on how to transition between the bulk theories.

Stratified factorization homology is a tool for constructing such theories with defects from their local coefficient systems. One well-motivated example is parabolic induction, in which $\operatorname{Rep}_q G$ is reduced to the $q$-commutative $\operatorname{Rep}_q T$ theory via Borel reduction along a defect. This is the stacky setting for Fock–Goncharov's cluster coordinates. It is also a natural context for constructing the quantum A-polynomial.

The talk will start with an introduction to stratified spaces and factorization homology, and will include a review of skein relations and categories. We will focus on surfaces with line defects, building the associated skein theory and discussing how it computes the relevant stratified factorization homology.