Defect Skein Theories

Abstract: 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.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

Topological Quantum Field Theory Club (IST, Lisbon)

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