Mathematical Sciences: Conformal Field Theories Associated with the Monster Simple Group

主要研究者将从事共形场的研究 与Monster简单群相关的理论。 这些将 提供了共形场论的第一个结构， orbifold对应于阶数大于 两个. 基于所有23个Niemaier格的构造将是 调查，与期望的线索，以协变量 构建基于26维的Moonshine模块 洛伦兹晶格就会出现。 主要研究者将 还研究了亏格零配分函数， 他最近发现的一些零星的群体。 一些 代数簇之间相互作用的新思想 并将寻求团体代表。 本研究涉及群论中的问题。 在对有限单群进行分类时，一个特别大的 一个叫做Monster Simple的群被发现了。 随后，发现Monster简单组 有趣的联系与李代数的研究， 数学物理 这个项目旨在更好地 理解这些关系。

The principal investigator will work on conformal field theories associated to the Monster simple group. These will provide the first constructions of conformal field theories on an orbifold corresponding to cyclic groups of order greater than two. Constructions based on all 23 Niemaier lattices will be investigated, with the expectation that clues to a covariant construction of the Moonshine module based on the 26-dimensional Lorentzian lattice will emerge. The principal investigator will also investigate the genus zero partition functions associated to certain sporadic groups which he has recently discovered. Some recent ideas involving the interplay between algebraic varieties and group representations will be pursued. This research is concerned with problems in group theory. In classifying the finite simple groups, a particularly large group which is called the Monster simple group was discovered. Subsequently, it has been found that the Monster simple group has interesting connections with the study of Lie algebras and with mathematical physics. This particular project is aimed at better understanding these relationships.