PIRSA:19100090 Scientific Series Mathematical physics

DOI10.48660/19100090

Series: Mathematical Physics

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_PIRSA:19100090,
  doi = {10.48660/19100090},
  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}}
}

Abstract

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.

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