Abstract:  The Remodeling Conjecture proposed by Bouchard-Klemm-Mariño-Pasquetti relates Gromov-Witten (GW) invariants counting holomorphic curves in a toric Calabi-Yau 3-manifold/3-orbifold to the Chekhov-Eynard-Orantin Topological Recursion (TR) invariants of its mirror curve. In this talk, I will describe the Remodeling Conjecture with descendants, which is a correspondence between all-genus equivariant descendant GW invariants and oscillatory integrals (Laplace transforms) of TR invariants along relative 1-cycles on the equivariant mirror curve. Our genus-zero correspondence is a version of equivariant Hodge-theoretic mirror symmetry with integral structures. In the non-equivariant setting, we prove a conjecture of Hosono which equates quantum cohomology central charges of compactly supported coherent sheaves with period integrals of a holomorphic 3-form along integral 3-cycles on the Hori-Vafa mirror. This talk is based on joint work with Bohan Fang, Song Yu, and Zhengyu Zong.