3D Mirror Symmetry and HOMFLY-PT Homology


Dimofte, T. (2019). 3D Mirror Symmetry and HOMFLY-PT Homology. Perimeter Institute. https://pirsa.org/19100090


Dimofte, Tudor. 3D Mirror Symmetry and HOMFLY-PT Homology. Perimeter Institute, Oct. 31, 2019, https://pirsa.org/19100090


          @misc{ pirsa_19100090,
            doi = {},
            url = {https://pirsa.org/19100090},
            author = {Dimofte, Tudor},
            keywords = {Mathematical physics},
            language = {en},
            title = {3D Mirror Symmetry and HOMFLY-PT Homology},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {oct},
            note = {PIRSA:19100090 see, \url{https://pirsa.org}}


A recent construction of HOMFLY-PT knot homology by Oblomkov-Rozansky has its physical origin in “B-twisted” 3D N=4 gauge theory, with adjoint and fundamental matter. Mathematically, the construction uses certain categories of matrix factorization. We apply 3D Mirror Symmetry to identify an A-twisted mirror of this construction. In the case of algebraic knots, we find that knot homology on the A side gets expressed as cohomology of affine Springer fibers (related but not identical to work if Gorsky-Oblomkov-Rasmussen-Shende). More generally, we propose a Fukaya-Seidel category mirror to the Oblomkov-Rozansky matrix factorization. Joint work with N Garner, J Hilburn, A Oblomkov, and L Rozansky.