Diagrammatics and Stratified Factorization Homology

par Dr Jennifer Brown (UC Davis)

mardi 13 juin 2023, 11:15 → 12:15 Europe/Paris

Pellos

It's known that skein categories give a diagrammatic description (i.e. one in terms of embedded graphs) of the homology theory which quantized character varieties of surfaces. Meanwhile, stratified factorization homology is a general machine for defining homology theories on spaces with singularities and defects. A version of skein theory which accounts for defects would give computational tools for quantizing the knot invariant known as the A-polynomial, in turn shedding light on the AJ conjecture.
 

 

This talk will start with a friendly introduction to stratified spaces and factorization homology, followed by a description of how skeins give the local algebraic data needed to define such a homology theory. It will also cover recent work to extend this construction to a setting with defects.

 

Time permitting, this will be followed by an explanation of the applications towards quantizing knot invariants.