Mathematical Sciences: Singularities in Determined AnalyticPDE and Associated Qualitative Properties of Solutions

首席研究员将研究 低维非线性真实的解析偏微分 方程他的方法的一个关键特点是使用 多值解和几何方法的研究 奇点研究的一个总目标是 偏微分方程几何不变量识别 控制解的奇异性 该奖项将支持一般领域的研究， 微分几何和全局分析。微分几何 是研究空间的几何形状 和空间上定义的分析概念。全球分析是 对物体的整体几何和拓扑性质的研究 一个空间，通过拼凑当地的信息。的应用 这些数学领域的其他科学包括 复杂的分子结构，液-气边界， 宇宙的大尺度结构

The principal investigator will study the singularities in low dimensional non-linear real analytic partial differential equations. A key feature of his approach will be the use of multivalued solutions and a geometric approach to the study of singularities. A general objective of the research will be to identify geometric invariants of partial differential equations which control singularities of solutions. 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.