Mathematical Sciences: Geometric Applications of Exterior Differential Systems

利用外微分方程组和偏微分方程组的几何知识，研究射影空间的子簇的性质。这些方法可能有助于在代数几何中的一些重要问题和猜想上取得进展。这项研究还需要开发某些算法系统的某些几何特征。这些问题的总体方法可能会延伸到纯数学和应用数学的其他分支。

The research entails questions concerning the properties of subvarieties of projective space using the geometry of exterior differential systems and partial differential equations. These methods may be instrumental in obtaining progress on some important questions and conjectures in algebraic geometry. The research also entails developing certain geometric features of certain algorithmic systems. The overall approach to these questions are likely to have extensions to other branches of pure and applied mathematics.