Geometric methods in representation theory and the Langlands program

表示论中的几何方法和朗兰兹纲领

• 批准号: DP150103525
• 负责人: A/Prof Ting Xue
• 金额: $ 43.47万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2015
• 资助国家: 澳大利亚
• 起止时间: 2015-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP150103525
• 关键词: Geometric; methods; representation; theory; Langlands

This research project aims to study questions in representation theory of groups using geometric methods. A central role is played by Langlands program which, broadly understood, can be viewed as a grand unified theory of mathematics. One setting for the work is modular representation theory with the aim of understanding irreducible characters. The project also aims to work on combinatorics and geometry in algebraic groups in small characteristics and one goal is to obtain a more uniform geometric understanding across all characteristics. The project also aims to work in the context of real groups and with the Gukov-Witten "fix of the orbit method" via branes. Finally, the project expects to begin a study of deformations of Galois representations in a general context.

本研究计画旨在利用几何方法研究群的表示论中的问题。朗兰兹纲领起着核心作用，广义地说，它可以被看作是数学的大统一理论。一个设置的工作是模块化表示理论的目的是了解不可约字符。该项目还旨在研究小特征代数群中的组合学和几何学，其中一个目标是在所有特征中获得更统一的几何理解。该项目还旨在在真实的群体的背景下工作，并通过膜与Gukov-Witten“固定轨道方法”。最后，该项目预计开始在一般情况下的变形伽罗瓦表示的研究。