## 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.

## Details

**Talk Number**PIRSA:19100090

**Speaker Profile**Tudor Dimofte

**Collection**Mathematical Physics

- Mathematical physics

**Scientific Area**

- Scientific Series

**Talk Type**