Mathematical Sciences: Geometries and Groups

证明了主要的可嵌入Lie关联几何的超平面都是由嵌入产生的。剩下的情况是对偶极空间，与例外李群相关的几何，以及半自旋几何的某些例外场。一类对形成关于Veldkamp空间的一般定理至关重要的几何也将被考虑。首席研究员将继续研究ım！-OVOID，它是极空间的OVOID和扩展的推广。这个项目的研究涉及有限维几何和变换群在这些几何上的作用之间的相互作用。这项工作对有限群的结构、代数编码理论和有限几何都有意义。

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.