Mathematical Sciences: Representation Theory of Reductive Groups

米尔科维奇教授将利用倒槽和D-模的思想来研究实还原群的表示理论。他的计划涉及许多项目，其中包括试图证明涉及特征圈的沃根猜想和研究表示的解析局部化。群论基本上是对称论。举一个简单的例子，当所讨论的系统在空间原点的位置改变时是不变的，自然就产生了翻译群。虽然群是抽象的对象，但特殊情况需要对称群的具体实现或“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.