Tudor Dimofte - 3d mirror symmetry and HOMFLY-PT homology
Recently, Gorsky-Negut-Rasmussen and Oblomkov-Rozansky proposed constructions of HOMFLY-PT link homology related to coherent sheaves on Hilbert schemes. Oblomkov-Rozansky explained how their construction was realized in several different physical systems, including (most relevantly for this talk) 3d supersymmetric gauge theories. I will discuss how a duality of 3d gauge theories known as 3d mirror symmetry -- whose mathematical/categorical implications are only starting to be explored -- acts on the setups above. The result is a very different, "A type" construction of link homology, related to cohomology of affine Springer fibers and to Hilbert schemes of points on singular curves. The talk will attempt to be fairly broad, with no prior technical knowledge assumed. Based on work with N. Garner, J. Hilburn, A. Oblomkov, and L. Rozansky; and related work of N. Garner and O. Kivinen.