Mathematical Sciences: Geometries and Groups

这项研究涉及的是表明，超平面的 主要的可嵌入Lie关联几何都来自于 嵌入 剩下的例子是对偶极空间， 与特殊李群相关的几何，以及某些 半自旋几何体的特殊场。 一类 形成关于Veldkamp的一般定理的关键几何 空间也将被考虑。 主要研究者将 继续努力吧！卵形体，这是两者的概括 卵形体和两极空间的扩展。 本项目的研究涉及以下因素之间的相互作用： 有限维几何和群的作用 在这些几何图形上进行变换。 这项工作具有影响 有限群的结构，代数编码理论 和有限几何学。

This research is concerned with showing that hyperplanes of the major embeddable Lie incidence geometries all arise from embeddings. The cases that remain are dual polar spaces, geometries associated with exceptional Lie groups, and certain exceptional fields for the half-spin geometries. A class of geometries crucial to forming general theorems about Veldkamp spaces will also be considered. The principal investigator will continue work on ım!-ovoids, which are generalizations of both ovoids and spreads of polar spaces. The research in this project involves the interplay between finite dimensional geometry and the actions of groups of transformations on these geometries. This work has implications for the structure of finite groups, for algebraic coding theory, and for finite geometry.