notes:2022-10-25-mina-aganagic-categorification-of-knot
Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| notes:2022-10-25-mina-aganagic-categorification-of-knot [2022/11/08 15:36] – removed - external edit (Unknown date) 127.0.0.1 | notes:2022-10-25-mina-aganagic-categorification-of-knot [2023/06/25 15:53] (current) – external edit 127.0.0.1 | ||
|---|---|---|---|
| Line 1: | Line 1: | ||
| + | ====== 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' | ||
| + | |||
| + | This talk will not be about super Lie-algebra, | ||
| + | |||
| + | |||
| + | ** Why we have quantum group ** | ||
| + | |||
| + | In 88Witten, Chern-Simon, | ||
| + | |||
| + | Conformal blocks, solutions to KZ equations | ||
| + | |||
| + | |||
| + | |||