Song Yu, Tsinghua YMSC

Title: Remodeling Conjecture with descendants

Abstract: The Remodeling Conjecture of Bouchard-Klemm-Mariño-Pasquetti obtains all-genus open-closed Gromov-Witten invariants of a toric Calabi-Yau 3-fold from Chekhov-Eynard-Orantin topological recursion on the mirror curve. In this talk, I will discuss an extension of this framework to descendant mirror symmetry, that is, the all-genus descendant Gromov-Witten invariants can be obtained from the Laplace transform of topological recursion invariants. The result is based on a correspondence between equivariant line bundles supported on toric subvarieties and relative homology cycles on the mirror curve, which provides an identification of integral structures. I will also discuss an application to Hosono’s conjecture if time permits. This talk is based on joint work in progress with Bohan Fang, Chiu-Chu Melissa Liu, and Zhengyu Zong.