Zhengyu Zong: All genus open-closed Crepant Transformation Conjecture for toric Calabi-Yau 3-orbifolds

Abstract: The Crepant Transformation Conjecture, proposed by Ruan, asserts certain equivalence between Gromov-Witten theory of two manifolds/orbifolds which are related by a crepant transformation. In general, the higher genus Crepant Transformation Conjecture is quite hard to study. Even the formulation of the Crepant Transformation Conjecture in the higher genus case is subtle. In this talk, I will explain the proof of the all genus Crepant Transformation Conjecture for general toric Calabi-Yau 3-orbifolds. We will consider the higher genus Gromov-Witten theory of toric Calabi-Yau 3-orbifolds in both open-string sector and closed-string sector. This talkis based on an ongoing project joint with Bohan Fang, Chiu-Chu Melissa Liu, and Song Yu.