该项目尝试运用微分拓扑和代数拓扑里的核心工具和想法来研究与紧黎曼面上稳定向量丛的模空间相关的一些几何拓扑问题。具体说来，我们关注于该模空间作为流形的一些几何拓扑不变量，用李群表示论和热核方程表达式来研究该模空间，以及一般紧凯勒流形上向量丛稳定性的拓扑推论和应用。

This project is to investigate some geometric and topological problems related to moduli spaces of stable vector bundles over Riemannian surfaces via the fundamental tools and ideas in differential and algebraic topology. More concretely, we are concerned with some geometric and topological invariants of these moduli spaces as manifolds, the investigation of these moduli spaces through representation theory and heat kernel of Lie groups, and topological implications and their applications of stability of general compact Kahler manifolds.