Mathematical Sciences: The Differential Geometry of PartialDifferential Equations

首席研究员将继续他对可积系统的研究。特别是，他将在分析与高阶网相关的G结构的结构方程的基础上，发展一种新的网理论。他还将研究Calabi-Yau三折模的几何和最小拉格朗日子流形的奇异性。该奖项将支持微分几何和全局分析领域的研究。微分几何是研究空间几何与空间上定义的解析概念之间关系的学科。全局分析是通过拼凑局部信息来研究空间的整体几何和拓扑特性。这些数学领域在其他科学中的应用包括复杂分子的结构、液气边界和宇宙的大尺度结构。

The principal investigator will continue his study of integrable systems. In particular he will develop a new theory of webs based on an analysis of the structure equations for the G- structure associated to a web of high rank. He will also study the geometry of the moduli of Calabi-Yau three folds and the singularities of minimal Lagrangian submanifolds. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.