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https://theias.zoom.us/j/83432499354?pwd=TkhMZWFJK2E1UzRyeUppU01pZVQwUT09**Abstract:** Khovanov showed, more than 20 years ago, that there is a deeper theory underlying the Jones polynomial. The``knot categorification problem” is to find a uniform description of this theory, for all gauge groups, which originates from physics. I found two solutions to this problem, related by a version of two dimensional (homological) mirror symmetry. They are based on two descriptions of the theory that lives on defects of the six dimensional (0,2) CFT, which are supported on a link times ``time".

In this talk, I will focus on the description in terms of A-branes, which is new and surprising. (While the B-brane description is new as well, it shares flavors of theories mathematicians discovered earlier.) The theory turns out to be solvable explicitly. In the Khovanov homology case, the A-model gives a way to compute it which is significantly more efficient than the algebraic descriptions mathematicians have found.

Event Description

Speaker

Mina Aganagic

Affiliation

University of California, Berkeley

Presentation

"Khovanov Homology from Mirror Symmetry"