Mathematical Sciences: Research in Representation Theory of Reductive Groups

点击翻译按钮获取中文摘要

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.