Title: Remodeling Conjecture and its recent developments

Abstract: The Remodeling Conjecture of Bouchard-Klemm-Mariño-Pasquetti is a framework for all-genus mirror symmetry for a toric Calabi-Yau 3-fold via Chekhov-Eynard-Orantin topological recursion on its mirror curve. In this talk, I will discuss recent extensions of this framework to 1) open Gromov-Witten invariants with boundary condition on multiple and possibly inner Aganagic-Vafa branes, 2) invariants with primary insertions, and 3) invariants with equivariant descendant insertions. This talk is based on joint work (partially in progress) with Bohan Fang, Chiu-Chu Melissa Liu, and Zhengyu Zong.