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

首席研究员将研究与Monster简单群相关的共形场理论。这将第一次在一个与大于2阶的循环群相对应的轨道上构造共形场论。基于所有23个尼迈耶晶格的结构将被研究，期望基于26维洛伦兹晶格的Moonshine模块协变结构的线索将会出现。首席研究员还将研究与他最近发现的某些零星群相关的属零配分函数。一些最近的想法涉及代数变量和群表示之间的相互作用将被追求。本研究涉及群论中的一些问题。在对有限单群进行分类时，发现了一个特别大的群，称为怪物单群。随后，人们发现怪物单群与李代数和数学物理的研究有着有趣的联系。这个特殊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.