Skein Categories and Quantization
Jennifer Brown
Abstract: The beautiful AJ conjecture predicts that a (yet-undefined) quantization of one knot invariant — the A-polynomial — annihilates another famous invariant, the colored Jones polynomial. This conjecture was formulated independently by both mathematicians and physicists, and is open but well supported.
The term "quantization" comes from physics, where it describes the transition from a classical to a quantum description of a system. Mathematically, it is a construction that deforms a commutative algebra into a non-commutative one.
The A-polynomial is constructed from the character variety of a knot's complement. We will describe recent work on quantizing this construction using skein categories, with the help of categorical actions, monads, and representable functors. This talk is based on joint work in progress with David Jordan and Tudor Dimofte.
category theory
Audience: researchers in the topic
( chat )
| Organizer: | Tim Hosgood* |
| *contact for this listing |