Mathematical Sciences: Group Theory and Combinatorics

这项研究致力于了解所谓的怪物集团。首席调查员将考虑三个方向。一是考虑《怪兽》的群性与某些经典模形式之间的关系。二是198684维空间中群的构造。三是用双曲线反射来表示群。本研究属于有限群论的一般领域。它关注的是研究一个特殊的群体，称为怪兽群体。这个群体没有被很好地理解，但有一个非常丰富的结构。目前，小组中的计算很困难，但只要成功地进行了计算，就会出现奇妙而简单的模式。这与数学的其他分支有很深的联系，而且很可能与理论物理也有同样的基本联系。

This research is concerned with understanding the so-called Monster Group. There are three directions which the principal investigator will consider. One is to consider the relations between the group-characters of the Monster and certain classical modular forms. The second is the constructions of the group in 198684-dimension space. the third is the representation of the group in terms of hyperbolic reflections. This research is in the general area of finite group theory. It is concerned with studying a particular group called the Monster Group. This group is not well understood but has a very rich structure. At present calculations in the group are difficult, but whenever they have been performed successfully, wonderful and simple patterns have emerged. There are deep connections with other branches of mathematics and it seems quite likely that there are equally fundamental connections with theoretical physics.