本项目主要研究辛拓扑和规范场理论中产生的与各种模空间有关的数学结构和不变量，如 Gromov-Witten 不变量普适方程和Virasoro猜想、约化Gromov-Witten不变量的计算、开Gromov-Witten理论与开弦、广义的Gromov-Witten理论、模空间的分解与不变量的计算、Donaldson理论、开闭弦的对偶、辛双有理几何、Floer同调理论、具有非紧结构群的杨-Mills理论、辛流形上哈密顿系统的周期轨道与紧流形上闭测地线、局部镜像对称等。这些问题的核心是与模空间有关的几何，分析，拓扑等性质的研究。本项目有望在这些课题的研究上取得重大进展。

In this project we will focus on various mathematical structures and invariants related to moduli spaces arising from symplectic topology and gauge theory, and will study the analytic, geometric and topological properties of these moduli spaces. The following problems will be investigated: Virasoro conjecture and universal equations for Gromov-Witten invariants, computations of reduced Gromov-Witten invariants, open Gromov-Witten invariants and open string theory, generalized Gromov-Witten theory，decompositions of moduli spaces and computations of invariants，Donaldson theory， duality between open and closed strings， symplectic birational geometry，Floer homology theory，Yang-Mills theory with non-compact structure groups, periodic orbits in Hamiltonian dynamics on symplectic manifolds and closed geodesics on compact manifolds, local mirror symmetry, etc.. It is hopeful that significant progress can be made in the study of these problems in the near future.