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

数学科学：黎曼曲面和模空间的谱几何

• 批准号: 9201669
• 负责人: Scott Wolpert
• 金额: $ 9.8万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9201669&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Spectral; Geometry; Riemann

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.

首席研究员将继续他在Teichmuller理论和光谱几何方面的研究。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。