Mathematical Sciences: Intertwining Operators, R-groups and Automorphic L-Functions

数学科学：交织算子、R 群和自同构 L 函数

• 批准号: 9501868
• 负责人: David Goldberg
• 金额: $ 5.58万
• 依托单位: Purdue Research Foundation
• 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 1998-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501868&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Intertwining; Operators; groups

This award supports research in number theory and representation theory. The principal investigator will work on determining the poles of standard intertwining operators attached to arbitrary maximal parabolic subgroups of quasi-split unitary groups and special orthogonal groups in odd dimensions. He will also continue research on the tempered spectrum of similitude groups. This award also supports the principal investigators efforts to establish a series of courses in number theory and representation theory. Number Theory is the study of properties of the whole numbers and is the oldest branch of mathematics. From the beginning problems in number theory have furnished the driving force to create new mathematics in almost all parts of the discipline. The Langland's program is a general philosophy that connects number theory with calculus. Modern number theory is very technical and deep, but has had astonishing applications in areas like theoretical computer science and coding theory.

该奖项支持数论和表象理论的研究。主要研究人员将致力于确定奇数维拟分裂酉群和特殊正交群的任意极大抛物子群上的标准交织算子的极点。他还将继续研究相似群体的回火频谱。该奖项还支持主要研究人员努力建立数论和表示理论的一系列课程。数论是研究整体数的性质的学科，是数学中最古老的分支。从一开始，数论中的问题就提供了在这门学科的几乎所有部分创造新数学的动力。朗兰德的计划是一种将数论和微积分联系起来的一般哲学。现代数论具有很强的技术性和深刻性，但在理论计算机科学和编码理论等领域有着惊人的应用。