Mathematical Sciences: Geometries & Groups

这个项目涉及有限几何和群体。 将考虑四个方面。 首席研究员将扩展以前的工作嵌入和超平面的点线几何;工作的特点parapolar空间;研究新的情况下的连接之间的m-蔓延和建设的广义四边形;并看看框架可以用来生成完整的李发病几何。 首席研究员将尝试在所有上述工作，以了解群体如何对几何形状的行动。 这个项目的研究涉及有限维几何和变换群对这些几何的作用之间的相互作用。 这项工作的影响有限群的结构，代数编码理论，有限几何。***

This project is concerned with finite geometries and groups. There are four areas which will be considered. The principal investigator will extend previous work on embeddings and hyperplanes of point-line geometries; work on characterizing parapolar spaces; study new cases of the connections between m-spreads and constructions of generalized quadrangles; and see if frames can be used to generate the full Lie incidence geometry. The principal investigator will attempt in all the above work to understand groups by how they act on geometries. 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. ***