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notes:2022-10-25-mina-aganagic-categorification-of-knot [2022/11/08 15:36] – removed - external edit (Unknown date) 127.0.0.1notes:2022-10-25-mina-aganagic-categorification-of-knot [2023/06/25 15:53] (current) – external edit 127.0.0.1
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 +====== 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. 
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 +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. 
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 +Conformal blocks, solutions to KZ equations
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 +