Mathematical Sciences: Differential Equations and Algebraic Groups and Their Representations - Discrete Subgroups of Semisimple Lie Groups

数学科学：微分方程和代数群及其表示 - 半单李群的离散子群

• 批准号: 8803289
• 负责人: V. Varadarajan
• 金额: $ 15.85万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8803289&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Differential; Equations; Algebraic

This project is mathematical research on Lie groups and their representations. Such groups, for instance the group of rotations of a sphere, are important because they embody the symmetries of situations that arise in many areas of mathematics. The present work is expected to have a high degree of contact with differential and algebraic geometry, with number theory, with differential equations, and with the theory of algebraic groups. More specifically, Professor Millson will study spaces of homomorphisms from a lattice in a Lie group to another Lie group, and will also pursue geometric questions concerning locally symmetric spaces associated to orthogonal and unitary groups. Professor Varadarajan will work on meromorphic differential equations, invariant differential equations and oscillatory integrals, and invariant analysis for reductive group actions.

这个项目是关于李群的数学研究， 他们的代表。 这样的群体，例如 球体的旋转是很重要的，因为它们体现了 在数学的许多领域中出现的对称性。 目前的工作预计将有高度的联系 微分和代数几何，数论， 微分方程和代数理论 组 更具体地说，米尔森教授将研究 从一个李群中的格到另一个李群的同态， 同时也将探讨一些几何问题， 与正交群和酉群相关的对称空间。 Varadarajan教授将研究亚纯微分 方程，不变微分方程和振动方程 积分和还原群作用的不变量分析。