Mathematical Sciences: Representation Theory

数学科学：表示论

• 批准号: 9101637
• 负责人: Herve Jacquet
• 金额: $ 14.08万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101637&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representation; Theory

This award supports the research of Professor H. Jacquet to work in automorphic functions. Professor Jacquet intends to study certain period integrals related to Gelfand triples using the relative trace formula. Modular forms arose out of Non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.

该奖项支持H. Jacquet教授在自同构函数方面的研究。Jacquet教授打算用相对迹公式研究与Gelfand三元组有关的某些周期积分。模形式起源于19世纪中期的非欧几里得几何。因此，数学家和物理学家很早就认识到，许多具有根本重要性的物体在其基本性质上是非欧几里得的。这个领域主要关注关于整数的问题，但在使用几何和分析时，它保留了与历史根源的联系，因此与理论物理中的规范理论和信息论中的编码理论等领域的问题联系在一起。