Mathematical Sciences: Differential Equations, Group Representations, and Mathematical Physics

数学科学：微分方程、群表示和数学物理

• 批准号: 9002579
• 负责人: V. Varadarajan
• 金额: $ 7.62万
• 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: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002579&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Differential; Equations; Group

Professors Varadarajan and Babbitt will work on a variety of projects. The first is a joint project involving the study of differential equations in a broad framework which relates them to algebraic groups and their representations. The questions to be studied have broad significance in such areas as differential modules over schemes, moduli of vector bundles, theory of algebraic groups, asymptotic analysis, and invariant differential operators and distributions. Other projects involve representation theory of the Poincare group, and scattering theory in the quantum Heisenberg model. The joint project focuses on the behavior of solutions to differential equations with singularities as a function of external parameters. The other projects fall under the heading of mathematical physics and involve mathematical aspects of quantum theory.

瓦拉达拉扬教授和巴比特教授将从事各种各样的项目。第一个是一个联合项目，涉及在一个将微分方程与代数群及其表示联系起来的广泛框架中研究微分方程。所研究的问题在方案上的微分模、向量束的模、代数群理论、渐近分析、不变微分算子和分布等领域具有广泛的意义。其他项目包括庞加莱群的表征理论和量子海森堡模型中的散射理论。该联合项目侧重于具有奇点的微分方程的解作为外部参数的函数的行为。其他项目属于数学物理的范畴，涉及量子理论的数学方面。