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

首席研究人员将致力于与怪兽简单群相关的保形场理论。这些将提供在对应于大于2的阶循环群的orforold上的共形场论的第一次构造。基于所有23个尼迈尔晶格的结构将被研究，期望基于26维洛伦兹晶格的月光模块的协变结构的线索将出现。首席研究员还将研究与他最近发现的某些零星散群有关的亏格零配分函数。本课程将探讨一些涉及代数簇和群表示之间相互作用的最新思想。这项研究涉及群论中的问题。在对有限单群进行分类时，发现了一个特别大的群，称为怪兽单群。随后，人们发现怪物单群与李代数的研究和数学物理有着有趣的联系。这个特别的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.