本项目主要研究融合系和有限群表示及其应用. 融合系是近年新发展起来的重要理论， 在有限群论、表示论和代数拓扑学等领域有深刻应用, 可望给出有限单群分类新的简化证明。 而有限群表示论近来十分活跃， 随着Brauer 高零猜想的解决，一些重大难题得到解决或出现重要突破， 特别是McKay 猜想归纳条件的给出，将推动 Algerin 权猜想和 McKay 猜想等问题的解决。 而线性群在高维Galois表示自守提升研究中的重要作用和群的偏差理论的发展， 使得线性群得以应用到Langlands 纲领和量子上同调、弦论等理论中，促进有关理论的发展。

We investigate fusion systems and group representations with their applications. The theory of Fusion systems is newly developed with deep applications in group theory, representation theory and algebraic topology, and possibly provides a simplified proof of the classification of finite simple groups. The representation theory of finite groups is very active in recent years, with Brauer Height zero conjecture solved so many breakthroughs occur in the study of most important open problems in this area. The inductive conditions on McKay conjecture will hopefully open the door to the solution of these related conjectures. Linear groups play a big role in the deviation theory of groups and in automorphy lifting of higher dimensional Galois representations and thus can be applied in the study of Langlands program and quantum cohomology and as well as string theory.