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

教授Varadarajan和Babalan将致力于各种 项目 第一个是一个联合项目，涉及研究 微分方程在一个广泛的框架，涉及到他们 代数群及其表示 问题是 研究在诸如差别化等领域具有广泛的意义， 概型上的模，向量丛的模，向量丛理论 代数群、渐近分析和不变微分 运算符和分布。 其他项目涉及 庞加莱群的表示理论和散射 量子海森堡模型中的理论。 该联合项目的重点是解决方案的行为， 奇异性为函数的微分方程 外部参数。 其他项目属于标题 数学物理学的一部分， 量子理论

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.