Mathematical Sciences: Local Harmonic Analysis With Applications To Automorphic Representations

谢尔斯塔德将继续她在扭曲内窥镜方面的工作，用于简化组。这是她帮助发展的自同构形式理论的一部分，并且基于约化李群的一般表示理论。它还计划发展实群上轨道积分的伊古萨理论。其目的是获得对自同构表示的重数公式有用的结果。李群理论是以挪威数学家索菲斯·李的名字命名的，一直是20世纪数学的主要主题之一。作为利用系统固有对称性的数学工具，李群的表示理论对数学本身，特别是在分析和数论方面，以及对理论物理，特别是量子力学和基本粒子物理，都产生了深远的影响。

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.