May 11: Song Yu

Title: The Open Crepant Transformation Conjecture for toric Calabi-Yau 3-orbifolds

Abstract:

I will discuss an open version of Ruan’s Crepant Transformation Conjecture, which is an identification of all-genus open-closed Gromov-Witten invariants of K-equivalent toric Calabi-Yau 3-orbifolds. Our approach is based on the mirror symmetry between toric Calabi-Yau 3-orbifolds and B-model mirror curves. I will first discuss the case of disk invariants, proven by the construction of a global family of mirror curves over the B-model moduli space and the disk mirror theorem of Fang-Liu-Tseng. I will then discuss ongoing joint work with B. Fang, C.-C. Liu, and Z. Zong on the general case based on the BKMP Remodeling Conjecture.