Mathematical Sciences: Representation Theory of Reductive Groups

Mirkovic教授将研究 真实的约化群使用反常层和D- 模块。 他的计划涉及许多项目，其中包括 试图证明沃根的一个猜想， 特征环和解析局部化的研究 表示。 群论基本上是对称性理论。 到 举一个简单的例子，当所讨论的系统是不变的时， 在空间原点的位置发生变化时， 翻译自然会出现。 虽然群体是抽象的， 对象，特殊情况需要具体实现或 对称群的“表示”。

Professor Mirkovic will study the representation theory of real reductive groups using the ideas of perverse sheaves and D- modules. His program involves a number of projects, among them an attempt to prove a conjecture of Vogan involving characteristic cycles and a study of analytic localization of representations. Group theory is basically the theory of symmetry. To take a simple example, when the system in question is invariant under a change in the position of the origin of space, the group of translations naturally arises. While groups are abstract objects, particular situations demand concrete realizations or "representations" of the symmetry group.