Talk at MSRI gauge theory workshop.

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