Mathematical Sciences: Singular Unitary Representations and Cohomology of Arithmetic Manifolds

数学科学：奇异酉表示和算术流形的上同调

• 批准号: 9501092
• 负责人: Jian-Shu Li
• 金额: $ 7.5万
• 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: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501092&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Singular; Unitary; Representations

DMS-9501092 PI: Li Li will investigate a new approach to the problem of exhaustion of automorphic forms based on recent work by Sarnak. This approach does not make use of Fourier coefficients and is applicable to groups of small rational rank, including anisotropic groups. It involves the study of matrix coefficients, small representations of p-adic groups, and some Diophantine problems. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.

DMS-9501092 PI：Li 李将研究一种新的方法来解决问题的用尽自守形式的基础上最近的工作Sarnak。 这种方法不使用傅立叶系数，适用于小有理秩的群，包括各向异性群。 它涉及到矩阵系数的研究，p-adic群的小表示，以及一些丢番图问题。 李群理论是以挪威数学家Sophus Lie的荣誉命名的，是世纪数学的重要课题之一。 李群表示论作为利用系统中固有对称性的数学工具，对数学本身，特别是分析和数论，以及理论物理学，特别是量子力学和基本粒子物理学产生了深远的影响。