====== 2022-10-25, Mina Aganagic, categorification of knot ======

Talk at MSRI gauge theory workshop. 


==== Khovanov homology and Jones polynomial ====
Given a knot or link in $\R^3$, Jones produces a 1-variable polynomial $J_K(q)$. 

Khovanov upgraded that polynomial to a bi-graded vector space, and taking Euler characteristics in one grading, put formal variable $q$ in the other grading, recovers Jones polynomial. The construction is very much functorial, compatible with knot cobordism. 

Knot categorification is about constructing maps from the category of colored points on a surface with morphism being merge and isotopy, to the category of representation of quantum groups $U_q(g)$. 

Webster already did this categorification. Here Mina gives a physics and A-model explanation why Webster's story works, and how to make it explicit. 

This talk will not be about super Lie-algebra, or non-simply laced ones, but just the simple ones. 


** Why we have quantum group **

In 88Witten, Chern-Simon, Hilbert space. 

Conformal blocks, solutions to KZ equations