Mathematical Sciences: Geometric Analysis and Spectral Invariants on Locally Symmetric Manifolds

数学科学：局部对称流形上的几何分析和谱不变量

• 批准号: 9104094
• 负责人: Robert Stanton
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9104094&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Analysis; Spectral

Professor Stanton's research project will apply noncommutative harmonic analysis and operator determinants to gain an understanding of holomorphic torsion on Hermitian locally symmetric manifolds. This effort, in collaboration with H. Moscovici, will focus on the current phase of the project which is to construct zeta functions associated to general rank spaces and to evaluate their special values in geometric terms. Another project, begun jointly with A. Knapp, will investigate certain differential operators on globally symmetric manifolds. This project will attempt to give a representation theoretic characterization of the solution space of these operators thereby resolving a conjecture of Vogan. A manifold is a generalization to higher dimensions of a smooth two dimensional surface. For example, the curved space-time continuum is a four dimensional manifold. Professor Stanton's research is aimed at understanding these geometric objects by exploiting connections with certain partial differential equations.

斯坦顿教授的研究项目将应用非交换 调和分析和算子行列式来获得一个 关于Hermite局部对称全纯挠的理解 流形 这项工作，在与H。威尔？莫斯科维奇 重点关注项目当前阶段的建设 zeta函数与一般秩空间相关联，并评估 它们在几何意义上的特殊价值。 另一个项目，开始 与A.克纳普，将调查某些差异 全局对称流形上的算子。 该项目将 试图给出一个代表性的理论表征的 这些算子的解空间，从而解决了 沃根 一个流形是一个更高维度的推广， 光滑的二维表面。 例如，弯曲的时空 连续体是四维流形。 斯坦顿教授的 研究的目的是了解这些几何物体， 利用与某些偏微分方程的联系。