T-equivariant disc potentials of toric manifolds

In this talk, we discuss how to derive the equivariant SYZ mirror of toric manifolds by counting holomorphic discs. In the case of (semi-)Fano toric manifolds, those mirrors recover Givental’s equivariant mirrors, which compute the equivariant quantum cohomology. Also, we formulate and compute open Gromov-Witten invariants of singular SYZ fiber, which are closely related to the open Gromov-Witten invariants of Aganagic-Vafa branes. This talk is based on joint work with Hansol Hong, Siu-Cheong Lau, and Xiao Zheng.

–Organized by Professor Shing-Tung Yau