Mathematical Sciences: Research in Representation Theory of Reductive Groups

本课题是李群表示理论的数学研究。后者的一个合适的例子是一个球体的旋转群。像这样的群很重要，因为它们作为对称群出现在数学的许多领域（例如几何、微分方程、代数数论、数学物理）。表征理论允许人们利用对称性来解决问题。米尔科维奇教授的工作将与代数、数论和几何有高度的联系。具体地说，他将研究在有限域上定义的约化群的表示，或实数，或正特征的全局域，使用d模和反常束的技术。

This project is mathematical research in the representation theory of Lie groups. A suitable example of the latter is the group of rotations of a sphere. Groups like this are important because they occur in many areas of mathematics ( e.g. geometry, differential equations, algebraic number theory, mathematical physics ) as groups of symmetries. Representation theory allows one to take advantage of symmetries in solving problems. The work of Professor Mirkovic will have a high degree of contact with algebra, number theory, and geometry. Specifically, he will investigate representations of reductive groups defined over finite fields, or the real numbers, or global fields of positive characteristic, using techniques of D-modules and perverse sheaves.