Seminar

Given a torus knot K in S^3, one can construct a Lagrangian L_K in the resolved conifold X under the conifold transition. On the other hand, the pair (X, L_K) corresponds to a mirror curve under mirror symmetry. There exist equivalences between the following three objects: The colored HOMFLY polynomial of K, the all genus open-closed Gromov-Witten theory of (X, L_K), and the topological recursion on the mirror curve. The above equivalences are given by the large N duality, mirror symmetry, and the matrix model for the torus knot respectively. In this talk, I will mainly focus on the mirror symmetry between the open-closed Gromov-Witten theory of (X, L_K) and the topological recursion on the mirror curve. I will also mention the other two equivalences if there is enough time. This talk is based on the paper 1607.01208 joint with Bohan Fang.