Mathematical Sciences: Topics in Analysis on Symmetric Spaces and Antomorphic Forms

数学科学：对称空间和拟形形式分析专题

• 批准号: 9207728
• 负责人: Svetlana Katok
• 金额: $ 5.04万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9207728&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Analysis; Symmetric

Professor Katok will work on several problems connected with automorphic forms. In particular, she will study the Fourier coefficients of non-holomorphic Maass forms. She will also study a generalization of Livshitz theory through the development of a higher cohomology theory for hyperbolic dynamical systems. Automorphic 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.

Katok教授将研究与以下方面有关的几个问题： 自守型 特别是，她将研究傅立叶 非全纯马斯形式的系数 她还将学习 通过发展一种新的 双曲动力系统的高阶上同调理论 自守形式产生于非欧几里德几何， 世纪中期。 数学家和 物理学家早就意识到， 基本的重要性是非欧几里德在其基本性质。 此字段主要涉及有关 整数，但在其使用的几何和分析，它 保留了与其历史根源的联系，从而与问题 从理论物理中的规范理论， 信息论中的编码理论