本项目计划研究辛几何、仿射微分几何和齐性空间中的一些整体问题。以等变的有理同伦论为工具，构造同辛结构和带tours群以Hamilton作用相关的代数模型，导出辛流形的性质；用仿射技巧和辛几何中的bubbling分析技巧研究仿射超曲面和射影Blaschke流形的性质和分类问题；借助于flag流形的painted Dynkin graph，用李代数和黎曼几何的技巧构造自然约化flag流形和测地轨道flag流形，进而进行分类。希望取得高水平的研究成果，在国际重要数学刊物上发表。

In this project we will study some global problems in symplectic geometry, affine differential geometry and homogeneous spaces. We will construct an algebraic type related symplectic structure and the Hamilton action by torus group, and derive characteristic of symplectic manifold. We will use the affine technique to study affine hypersurfaces and projective Blaschke manifolds. We will use the painted Dynkin graph and the technique of Riemannian geometry to find the examples of naturally reductive flag manifolds and geodesic orbits flag manifolds and to classify them. We hope to obtain outstanding results and publish them on famous mathematical journals.