Mathematical Sciences: Local Harmonic Analysis With Applications To Automorphic Representations

谢尔斯塔德将继续她的工作扭曲内窥镜， 还原群 这是自守理论的一部分 她在发展中发挥了重要作用， 关于约化李群的一般表示论。 还计划发展轨道积分的Igusa理论 在真实的群体中。 目标是获得有用的结果， 自守表示的重数公式。 李群理论，以挪威人的荣誉命名 数学家Sophus Lie，一直是 世纪数学。 作为数学工具， 利用系统中固有的对称性， 李群的表示理论对 数学本身，特别是在分析和数字方面， 理论和理论物理学，特别是量子 力学和基本粒子物理学。

Shelstad will continue her work on twisted endoscopy for reductive groups. This is a part of the theory of automorphic forms which she has been instrumental in developing, and is based on the general representation theory of reductive Lie groups. It is also planned to develop Igusa theory for orbital integrals on real groups. The goal is to obtain results useful for multiplicity formulas for automorphic representations. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.