He has conducted a series of influential research works in the following directions:
1. Topological Vertex Theory: Together with collaborators, he established the mathematical theory of the Topological Vertex. This work mathematically proves the duality proposed by physicists between Chern-Simons theory and the Gromov-Witten theory of certain 3-dimensional Calabi-Yau spaces. For these contributions, he was invited to deliver a one-hour plenary lecture at the International Congress of Chinese Mathematicians (ICCM).
2. LG/CY Correspondence for Elliptic Genera: In collaboration with students, he developed a method based on the Residue Theorem to establish the LG/CY correspondence for elliptic genera. This work inspired physicists (such as Hori and others) to establish residue formulas for the elliptic genera of 2D gauged linear sigma models.
3. BKMP Conjecture and Emergent Geometry: He obtained the first results regarding the BKMP Conjectureon the Eynard-Orantin topological recursion for toric Calabi-Yau 3-folds and derived the corresponding first batch of quantum spectral curves. Building on this work, he proposed the concept of Emergent Geometry, introducing ideas from statistical physics into this field.
4. Dessins d'Enfants and Duality: His recent research investigates the duality between Grothendieck’s dessins d’enfants and various models arising in superstring theory.
Publications: His representative papers have been published in leading mathematical journals such as the Journal of the American Mathematical Society (JAMS), Journal of Differential Geometry (JDG), Journal of Algebraic Geometry (JAG), and Advances in Mathematics, as well as in mathematical physics journals including Journal of High Energy Physics (JHEP).
