| Abstract: |
Using string theory, Ooguri and Vafa showed that the HOMFLYPT polynomials of a link in the 3-sphere are equivalent to the count of holomorphic curves in the resolved conifold with boundary on a certain Lagrangian submanifold. Recently, Ekholm and Shende introduced a mathematically rigorous framework of Gromov-Witten counts of bordered holomorphic curves that take values in the skein module of the Lagrangian and recovered the result of Ooguri and Vafa. In this talk, I will present joint work with P. Longhi and T. Ekholm analyzing the Gromov-Witten invariants of Lagrangians associated to the Hopf link. We exhibit operators acting on the skeins of the Lagrangians which annihilate the GW-partition functions. Using these operators, we compute the GW-partition functions and show that they decompose into elementary partition functions. The decompositions we obtain are reminiscent of the Gopakumar-Vafa formula and the knots-quivers correspondence.
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