Knot categorification from homological mirror symmetry

          @misc{ scivideos_PIRSA:22060016,
            doi = {10.48660/22060016},
            url = {https://pirsa.org/22060016},
            author = {Aganagic, Mina},
            keywords = {Mathematical physics},
            language = {en},
            title = {Knot categorification from homological mirror symmetry},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2022},
            month = {jun},
            note = {PIRSA:22060016 see, \url{https://scivideos.org/pirsa/22060016}}
          }
          

Abstract

"Khovanov showed in ‘99 that the Jones polynomial arises as the Euler characteristic of a homology theory. The knot categorification problem is to find a general construction of knot homology groups and to explain their meaning: what are they homologies of? Homological mirror symmetry, formulated by Kontsevich in ’94, naturally produces hosts of homological invariants. Sometimes, it can be made manifest, and then its striking mathematical power comes to fore. Typically though, it leads to invariants which have no particular interest outside of the problem at hand. I will explain that there is a vast new family of mirror pairs of manifolds for which homological mirror symmetry does lead to interesting invariants, and solves the knot categorification problem. "