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Dissertation Defense – Luke Conners
February 12 @ 4:00 pm - 5:30 pm
Colored Torus Link Homology
The package of Type A link homology theories is controlled by (Type A) singular Soergel bimodules. We introduce several families of “Fray” functors on singular Soergel bimodules, modeled on constructions in categorical representation theory. We prove that each of these families gives rise to a corresponding family of column-colored link homologies interpolating between existing constructions of column-colored homology. Finally, we use Fray functors to compute the column-colored HOMFLY homology of positive torus knots, resulting in the first verification of mirror symmetry conjectures for colored HOMFLY homology in nontrivial colors.
This talk is based on our work “Row-column mirror symmetry for colored torus knot homology” (C. 2024, Sel. Math., vol. 30 no. 97) and “Fray functors and equivalence of colored HOMFLYPT homologies” (C. 2024, arXiv:2405.00875).