Mathematical Sciences: Real Submanifolds and Holomorphic Functions

首席研究员将专注于多复变量函数理论的两条研究路线。他将研究实函数的全纯辛几何和实子流形的全纯接触几何。他还将研究CR结构和CR向量束的可积性问题的一个特解的正则性。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 focus on two lines of research in the theory of functions of several complex variables. He will study the holomorphic symplectic geometry of real functions and the holomorphic contact geometry of real submanifolds. He will also study the regularity of a particular solution to the integrability problem for CR structures and for CR vector bundles. 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.