Mathematical Sciences: Finite Groups and Elliptic Cohomology

这个项目涉及到理论的扩展 Thompson级数到椭圆模。这是一个设备， 将有限群的表示理论与椭圆群的表示理论联系起来 模形式它在各个领域都有影响， 数学，如散在单群理论， 流形拓扑和椭圆上同调。特别是， Hecke算子作为椭圆算子作用 上同调，以及一个约束椭圆模的存在性 将检查Monster简单组的亏格零。 这个项目是在有限群的一般领域 理论它将研究群论和 数论这项工作有望对 理论物理学和数学

This project is concerned with an extension of the theory of Thompson series to elliptic modules. This is a device which relates representation theory of finite groups with elliptic modular forms. It has consequences in various areas of mathematics such as the theory of sporadic simple groups, topology of manifolds, and elliptic cohomology. In particular, the role of Hecke operators as operations in elliptic cohomology, and the existence of a conjectured elliptic module of genus zero for the Monster simple group will be examined. This project is in the general area of finite group theory. It will examine connections between group theory and number theory. This work promises to have consequences for theoretical physics, as well as, mathematics.