# 3D Mirror Symmetry and HOMFLY-PT Homology

### APA

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

### MLA

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

### BibTex

@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}} }

Tudor Dimofte University of Edinburgh

## 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.