本项目主要研究微分几何和几何分析中产生的几何奇点和相关的正则性问题，如Kaehler几何中的典则度量存在性，Ricci流，轨形的几何分析理论，奇点的不变量与代数几何中的稳定性等。这些问题的核心是与各种奇点有关的几何，分析，拓扑等性质的研究，研究领域涉及多复变中的位势理论， 偏微分方程中实和复Monge-Ampere型方程， 代数几何中的几何不变量理论、模空间理论以及奇点形变理论， 几何分析中的Ricci流等的研究课题。本项目有望在这些课题研究中取得重大进展。

In this project we will focus on various problems on geometric singularity and the related regularity in differential geometry and geometric analysis. The following problem will be investigated: existence of canonical metrics in Kaehler geometry, Ricci flow, geometric analysis theory of orbifolds, invariants of singularities and stabilities in algebraic geometry, etc. The main ingredients are the geometrical, analytical and topological properties of various singularities. The study covers potential theory in complex variables, real and complex Monge-Ampere typed equations in PDE, geometric invariant theory, moduli space theory, and singularity theory in algebraic geometry, and Ricci flow in geometric analysis. It is hopeful that significant progress can be made in the study of these problems in the near future.