Mathematical Sciences: Group Theory and Combinatorics

这项研究是关于了解所谓的怪物集团。主要研究者会考虑三个方向。一是考虑怪物的群字与某些经典模形之间的关系。二是198684维空间中的群体建构。第三是用双曲反射来表现群体。本研究属于有限群论的一般范畴。它关注的是研究一个被称为怪物群体的特殊群体。这个群体还没有被很好地理解，但结构非常丰富。目前，这个小组的计算是困难的，但每当他们成功地进行计算时，就会出现奇妙而简单的图案。它与数学的其他分支有着深刻的联系，似乎很可能与理论物理学有着同样基本的联系。

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.