Mathematical Sciences: Local Harmonic Analysis with Applications to Automorphic Repressentations

Shelstad将研究局部域上连通的约化代数群的扭曲内窥镜。计划发展传递因子的下降理论，并将其应用于扭轨积分传递中的一些关键问题。总体目标是建立适用于阿德尔扭迹公式的稳定化和自同构表示的研究结果，特别是复形公式。李群理论是为了纪念挪威数学家索夫斯·李而命名的，它一直是20世纪数学的主要主题之一。作为利用系统中固有对称性的数学工具，李群表示理论对数学本身，特别是分析和数论，以及理论物理，特别是量子力学和基本粒子物理产生了深远的影响。

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.