Algebraic Geometry Seminar: Hsian-Hua Tseng

Abstract: For a toric manifold X and a Lagrangian torus fiber L in X, Fukaya-Oh-Ohta-Ono defined open Gromov-Witten invariants which are virtual enumerations of holomorphic disks in X with boundary conditions in L. Qualitative and quantitative properties of these open Gromov-Witten invariants play important roles in the symplectic geometry and mirror symmetry of X. Open Gromov-Witten invariants are difficult to compute because standard methods in Gromov-Witten theory (such as virtual localization) are not applicable. In this talk we explain a geometric method that leads to a complete calculation of these open Gromov-Witten invariants for compact semi-Fano toric manifolds. This is joint work with K. Chan, S.-C. Lau, N. C. Leung.