Representation Theory and Automorphic Forms

AbstractSpeh/Barbasch教授Barbasch将研究还原群的幂幺表示的性质，例如它们的酉性及其与自守形式和轨道方法的关系。 他将继续与A. Moy和S. evens在相关的主题。Speh教授将继续与J. Rohlfs共同研究Eisenstein上同调，旨在计算Tamagawa数并获得周期积分的合理性结果。她将与Dan Barbasch一起继续研究从扭曲的内窥镜组中提升自守形式。比尔吉特斯佩也将继续她的工作塞伯格-威滕方程和扭曲torsion. This建议属于一般领域的代表性理论李群及其应用自守形式福尔斯。李群（以挪威数学家Sophus Lie的荣誉命名）及其表示理论是20世纪世纪数学的重要课题之一。 作为利用系统中固有对称性的数学工具，李群的表示理论在分析和理论物理学中产生了深远的影响，特别是量子力学和基本粒子物理学。现代形式的自守形式理论是由Gelfand、Piatetski-Shapiro、Langlands和Borel发起的，并且在很大程度上依赖于李群的表示理论。它对经典数论中出现的问题产生了重大影响，并有望继续这样做。 这些理论非常抽象，但在理论计算机科学和编码理论等领域有着令人惊讶的重要应用。

AbstractSpeh/BarbaschProfessor Barbasch will investigate properties of unipotent representations of reductive groups such as their unitarity and their relation to automorphic forms and the orbit method. He will continue his joint work with A. Moy and S. Evens on related topics. Professor Speh will continue her joint work with J. Rohlfs on Eisenstein cohomology aiming to compute Tamagawa numbers and obtain rationality results for periods integrals. Jointly with Dan Barbasch she will continue work on lifting automorphic forms from twisted endoscopic groups. Birgit Speh will also continue her work on Seiberg-Witten equations and twisted torsion.This proposal falls in the general area of representation theory of Lie groups and its applications to automorphic forms. Lie groups (named in honor of the Norwegian mathematician Sophus Lie) and their representation theory, have 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 in analysis and theoretical physics, especially quantum mechanics and elementary particle physics. The theory of automorphic forms in its modern form was initiated by Gelfand, Piatetski-Shapiro, Langlands and Borel and relies heavily on the representation theory of Lie groups. It has had a significant impact on problems arising in classical number theory and is expected to continue to do so. These theories are very abstract, but have surprising important applications in areas like theoretical computer science and coding theory.