Subtle Symmetries and the Refined Monster

微妙的对称和精致的怪物

• 批准号: DP160104912
• 负责人: Dr Nora Ganter
• 金额: $ 15.77万
• 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: 2016
• 资助国家: 澳大利亚
• 起止时间: 2016-06-30 至 2020-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP160104912
• 关键词: Subtle; Symmetries; Refined; Monster

The project plans to develop a new conceptual framework for the representations and characters of categorical groups. The field of representation theory exploits the symmetries of an object (eg a molecule) in order to facilitate its study. This project aims to investigate the case where the symmetries themselves are related by symmetries. Traditionally often ignored, this subtle but powerful information turns out to be at the heart of various deep phenomena. It is anticipated that the project’s approach recasts and simplifies some important and difficult mathematics, providing a new approach to affine representation theory, to the foundations and symmetries of string theory, and the Refined Monster Conjecture.

该项目计划为分类群体的表征和特征开发一个新的概念框架。表示论领域利用物体（例如分子）的对称性来促进其研究。该项目旨在研究对称性本身通过对称性相关的情况。这种微妙但强大的信息传统上经常被忽视，但事实证明它是各种深层现象的核心。预计该项目的方法将重新设计和简化一些重要且困难的数学，为仿射表示论、弦理论的基础和对称性以及精炼怪物猜想提供一种新方法。