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.

Varadarajan教授和Babbitt将从事各种项目。 第一个是一个联合项目，涉及广泛框架中微分方程的研究，将它们与代数群体及其表示相关。 要研究的问题在诸如方案的差异模块，矢量束模量，代数群体理论，渐近分析以及不变的差分运算符和分布等领域具有广泛的意义。 其他项目涉及庞加雷群体的代表理论，以及量子海森堡模型中的散射理论。 联合项目着重于具有奇异性与外部参数函数的微分方程解决方案的行为。 其他项目属于数学物理学的标题，涉及量子理论的数学方面。