Automorphic Forms on Higher Rank and Kac-Moody Groups

高阶群和 Kac-Moody 群上的自守形式

• 批准号: 1500562
• 负责人: Stephen Miller
• 金额: $ 7.5万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1500562&HistoricalAwards=false
• 关键词: Automorphic; Forms; Higher; Rank; Kac

Automorphic forms are a basic yet intricate structure in modern mathematics. Though historically they have been studied primarily by number theorists and representation theorists, they have connections to other branches of science. This research explores a number of questions connecting different areas of mathematics and physics. The project includes collaborative work with mathematical physicists that uses automorphic forms to describe corrections to general relativity that arise in string theory. Other projects include a detailed investigation of the square-integrability of certain Eisenstein residues (which has applications to the unitary dual problem), as well as a study of Eisenstein series on infinite-dimensional Kac-Moody group (in particular, the meromorphic continuation of their constant terms). Another project concerns applications of Voronoi-style summation formulas to number theory, such as to subconvexity problems for automorphic L-functions. Finally, the Miatello-Wallach conjecture (that the moderate growth condition in the theory of automorphic forms is in fact redundant on higher rank groups) will also be a focus of the research.

自动形式是现代数学中的基本但复杂的结构。 尽管从历史上看，它们主要是由数字理论家和代表理论家研究的，但它们与其他科学分支机构有联系。 这项研究探讨了许多连接数学和物理领域的问题。 该项目包括与数学物理学家的合作工作，这些数学物理学家使用自动形式形式来描述字符串理论中出现的一般相对性的校正。其他项目包括对某些Eisenstein残基（对单一双重问题的应用）的详细研究，以及对Eisenstein系列无限维kac-moody群体的研究（尤其是其恒定项的meromormorphtic延续）。 另一个项目涉及Voronoi风格的求和公式对数字理论的应用，例如针对自动型L功能的亚概念问题。最后，Miatello-Wallach的猜想（实际上，自动形式理论中的中等生长条件实际上在高级组上是多余的）也将是研究的重点。