Mathematical Sciences: Local Harmonic Analysis with Applications to Automorphic Repressentations

DMS-9500880 PI：谢尔斯塔德·谢尔斯塔德将研究局部区域上连通还原代数群的扭曲内窥镜。计划发展转移因子的下降理论，并将其应用于扭转轨道积分转移中的一些关键问题。一个总的目标是建立适用于adelic扭曲迹公式的稳定化和自同构表示的研究的结果，特别是重数公式。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。

DMS-9500880 PI: Shelstad Shelstad will investigate the twisted endoscopy of connected reductive algebraic groups over local fields. It is planned to develop descent theory for transfer factors and applying it to some pivotal questions in transfer of twisted orbital integrals. An overall goal is to establish results applicable to stabilization of the adelic twisted trace formula and the study of automorphic representations, especially multiplicity formulas. 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.