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Remodeling conjecture and its application

The remodeling conjecture relates the open-closed Gromov-Witten invariants of a toric Calabi-Yau 3-orbifold to the topological recursion on its mirror spectral curve. I will describe the set up of this conjecture and outline of its proof, then I will explain, by examples, how such conjecture could imply the crepant transformation conjecture and the modularity properties of Gromov-Witten invariants. This talk is based on the joint work with Chiu-Chiu Melissa Liu and Zhengyu Zong, and on the joint work with Yongbin Ruan, Yingchun Zhang and Jie Zhou.