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Torus knots, open Gromov-Witten invariants, and topological recursion
Algebraic Geometry and Number Theory| Speaker: | Zhengyu Zong, Tsinghua University |
| Related Webpage: | http://ymsc.tsinghua.edu.cn/content.asp?channel=2&classid=9&id=2989 |
| Location: | 3106 MSB |
| Start time: | Thu, Apr 5 2018, 1:10PM |
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 arXiv:1607.01208 joint with Bohan Fang.