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3D Mirror Symmetry and HOMFLY-PT Homology

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.

COVID-19 information for PI Residents and Visitors

Collection/Series: 
Event Type: 
Seminar
Scientific Area(s): 
Speaker(s): 
Event Date: 
Thursday, October 31, 2019 - 13:30 to 15:00
Location: 
Sky Room
Room #: 
394