Mathematical Sciences: Representations & Cohomology of Finite & Compact Lie Groups

这个奖支持有限紧李群的表示和上同调的研究。有三个领域将被调查。第一部分主要研究了有限群在素数特征域上的表示理论和上同调。第二部分涉及到通过从有限情况扩展现有方法来理解紧李群的上同调。第三部分是构造有限李群和紧李群的分类空间之间的映射。本研究支持有限群的表示理论。群是用来研究变换的代数对象。正因为如此，分组是物理、化学、计算机科学以及数学的基本工具。表征理论是确定群体结构的重要方法。＊＊＊

Benson This award supports work on representations and cohomology of finite and compact Lie groups. There are three areas which will be investigated. The first is an investigation of the representation theory and cohomology of finite groups, primarily over fields of prime characteristic. The second involves understanding the cohomology of compact Lie groups, by extending current methods from the finite case. The third is aimed at constructing maps between classifying spaces of finite and compact Lie groups. 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. ***