Mathematical Sciences: Modular Representations of Finite Groups

该奖项涉及代表理论， 素特征域上有限群的上同调 特别令人感兴趣的是以下的同调性质： 基本模块理论的基础表示和 作用于群的上同调环的结构 基本的同调结构 校长 研究人员计划研究的主要理想是 上同调元的零化子及其与 从组的子组转移和限制。 分类技术，以及超上同调谱 序列与某些对偶复合体和行动的 Steenrod代数，将用于这项研究。 其他 关于模块结构的问题， 此外，我们亦会研究范畴设置。 此外该 首席研究员将继续研究同源性 Hilbert模代数及其计算机方法 上同调的计算 该研究支持的是表征理论， 有限群 群是用来研究的代数对象 转变 正因为如此，群体是一个基本的工具 在物理、化学和计算机科学方面， 数学 表示论是一种重要的方法， 决定群体的结构。

This award is concerned with the representation theory and cohomology of finite groups over fields of prime characteristic. Of particular interest are the homological properties of representations which underlie the basic module theory and the structure of the cohomology ring of the group which acts on the fundamental homological constructions. The principal investigator plans to study the prime ideals which are the annihilators of cohomology elements and their relations to transfers from and restrictions to subgroups of the group. Categorical techniques, as well as hypercohomology spectral sequences associated to certain duality complexes and actions of the Steenrod algebra, will be used for this investigation. Other questions on the structure of modules in the more general categorical setting will also be examined. In addition, the principal investigator will continue work on the homological algebra of Hilbert modules and on computer methods for the computation of cohomology. The research supported concerns the representation theory of finite groups. A group is an algebraic object used to study transformations. Because of this, groups are a fundamental tool in physics, chemistry and computer science as well as mathematics. Representation theory is an important method for determining the structure of groups.