Subtle Symmetries and the Refined Monster

该项目计划开发一个新的概念框架的表示和性质的类别组。表示论领域利用物体（如分子）的对称性来促进其研究。本项目旨在研究对称性本身与对称性相关的情况。传统上经常被忽视，这种微妙但强大的信息原来是各种深层现象的核心。预计该项目的方法重铸和简化了一些重要和困难的数学，为仿射表示论、弦理论的基础和对称性以及精化怪物猜想提供了一种新的方法。

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.