My research area is geometry and mathematics related to string theory. More precisely, I am interested in mathematical theories related to N = (2, 2) supersymmetric quantum field theory. Mathematically, Gromov-Witten invariants virtually count stable (or orbifold stable) maps to projective varieties and symplectic manifolds (or symplectic orbifolds). It gives a description for the non-linear sigma model. Fan-Jarvis-Ruan-Witten invariants virtually count solutions of Witten equations and can be viewed as a mathematical description for Landau-Ginzburg model of quasi-homogeneous hypersurface singularities. Currently, my works focus on Gromov-Witten theory, Fan-Jarvis-Ruan-Witten theory and global mirror symmetry in a broad sense, including topics such as Landau-Ginzburg/Calabi-Yau correspondence, integrable hierarchies and number-theoretic aspect of Gromov-Witten theory.