Mathematical Sciences: Spectral Geometry for Riemann Surfaces and the Moduli Space

首席研究员将继续他在泰希穆勒理论和谱几何方面的研究。他将考虑三个新的主题：谱的退化，Rankin-Selberg L函数的特殊值，以及Teichmuller空间的映射类群不变泊松核。该奖项将支持在微分几何和全球分析的一般领域的研究。微分几何是研究空间几何和定义在该空间上的解析概念之间的关系的学科。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性质的学科。这些领域的数学在其他科学中的应用包括复杂分子结构、液体-气体边界和宇宙的大尺度结构。

The principal investigator will continue his research in Teichmuller theory and spectral geometry. He will consider three new topics: degeneration of the spectrum, special values of Rankin-Selberg L-functions, and a mapping class group invariant Poisson kernel for the Teichmuller space. 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.