Mathematical Sciences: Group Theory and Buildings

本研究关注的是双子建筑和Kac-Moody 组 这项工作的主要目的是对 至少有三个等级的双子建筑， Kac-Moody类型，对他们进行操作。 主要研究者 还将研究仿射建筑物的局部-全局特性， 双曲线建筑的整体结构 所支持的研究是在一个关键领域， 数学的各个部分是相互交叉的。 该项目致力于 利用有限几何对某些有限群进行分类， 组合学 几何学上的联系 约化代数群和Kac-Moody群对于 对有限单群的研究。

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.