ABSTRACT: In this talk, I will discuss an ongoing joint project with Zhengyu Zong on the Gromov-Witten/Donaldson-Thomas correspondence for local gerby curves, as an orbifold generalization of the corresponding work on the smooth case by Bryan-Pandharipande and Okounkov-Pandharipande. By applying degeneration formulas, the correspondence can be reduced to the case of [C^2/Z_{n+1}] \times P^1, where the 3-point relative GW/DT invariants can be related to the quantum multiplication by divisors for Hilb([C^2/Z_{n+1}] and Sym([C^2/Z_{n+1}]). This is a crepant resolution counterpart to the work of Maulik-Oblomkov and Cheong-Gholampour.