有限群及其表示论是一门有着悠久历史，同时又充满活力的学科。随着现代数学的发展，几何化和范畴化的思想在数学的各个领域得到越来越多的重视，代表了数学发展的方向和趋势。在这样一个大的背景下，本项目主要研究有限群及其表示理论的范畴化，具体表现在两个方面的探讨上：融合系统和2-表示。上述两个方向，虽然都是新兴的研究领域，但是最近几年受到了国际上来自不同领域的专家的共同关注，特别是近两年不断有相关的文章发表在一流的数学杂志上。有鉴于这两个方向发展的现状与特点，在本项目中，我们将以融合系统和2-表示理论体系的构建与完善为研究的主线，同时结合上述理论在模表示论中，特别是模表示论三大支柱猜想中的应用来展开研究工作。除了范畴化思想，本项目的研究工作将涉及到范畴论、群论、表示论、同伦论以及微分拓扑等领域，反映了其多学科交叉与融合的特点。因此，本项目的成果也必将对上述相关领域起到良好的推动作用。

It is well-known that the long established theory, finite group and its representation theory, is an activated field. With the development, the geometrification and categorification are more and more important in all of branches of mathematical science which is the new trend in the modern research. In this project, we focus on the categorification of finite group theory and its representation: fusion system and 2-representation. Though both of the two topics are emerging areas of mathematics, many experts in different areas have pay much more attention to them and many articals on these topics are published in the top-level mathematical journals. In the project, we will try to study these systematically to improve the foundations of these theories. We also consider their applications to the investigation of main conjecturs in modular representation theory. This project involves category theory, group theory, representation theory, homotopy and differential topology. So there is no doubt that this project will give positive reaction on these areas.