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

瓦拉达拉扬教授和巴比特教授将致力于各种项目。第一个是一个联合项目，涉及在一个广泛的框架内研究微分方程式，将它们与代数群及其表示法联系起来。所要研究的问题在格式上的微分模、向量丛的模、代数群论、渐近分析、不变微分算子和分布等领域具有广泛的意义。其他项目涉及庞加莱群的表象理论，以及量子海森堡模型中的散射理论。联合项目的重点是作为外部参数的函数的奇异性微分方程解的行为。其他项目属于数学物理的范畴，涉及量子理论的数学方面。

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.