Mathematical Sciences: Geometries & Groups

这个项目是关于有限几何和群。将考虑四个方面。首席研究员将扩展先前在点线几何的嵌入和超平面方面的工作；研究抛物线空间的特征；广义四边形结构与m-扩展之间联系的新情况研究看看是否可以用帧来生成完整的李氏入射几何。在上述所有工作中，首席研究员将尝试通过群体对几何图形的作用来理解群体。本项目的研究涉及有限维几何与这些几何上的变换群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影响。＊＊＊

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. ***