Mathematical Sciences: Group Theory and Buildings

这项研究是关于双子建筑和Kac-Moody集团的。这项工作的主要目标是对至少三级的双子建筑进行分类，并对其进行Kac-Moody类型的分组操作。首席研究员还将研究仿射建筑的局部-全局特性和双曲建筑的全局结构。所支持的研究是在数学的几个部分交叉的一个关键领域。这个项目试图用有限几何和组合学对某些有限群进行分类。与代数群和Kac-Moody群理论的几何联系对于研究有限单群具有重要意义。

This research is concerned with twin buildings and Kac-Moody groups. The main thrust of the work is towards a classification of twin buildings of rank at least three, and the groups of Kac-Moody type which operate on them. The principal investigator will also study local-global properties of affine buildings and the global structure of hyperbolic buildings. The research supported is in a crucial area where several parts of mathematics intersect. This project endeavors to classify certain finite groups by using finite geometry and combinatorics. The geometric connection to the theory of reductive algebraic groups and Kac-Moody groups is important for the study of finite simple groups.