Mathematical Sciences: Group Theory and Combinatorics

本研究针对组合学和群论中的几个问题。首席研究员将考虑球体填充问题的基本原理，低维晶格的应用，以及Monster简单群。球体打包工作已经导致了一项量化特定类型代码的专利，但长期的优点是导致了怪物简单群和怪物之间的联系。这个项目涉及组合学和群论中的问题。特别是，首席研究员将专注于一个特别引人注目的群体，它被称为“怪物”。这项研究的结果可能会影响数学和物理的其他领域。

This research is directed at several problems in combinatorics and group theory. The principal investigator will consider the fundamentals of the sphere packing problem, applications of low dimensional lattices, and the Monster simple group. The sphere packing work has already led to a patent on quantizing a certain type of code but the long term merit is in leading to connections between the Monster simple group and the Monster. The project is concerned with problems in combinatorics and group theory. In particular, the principal investigator will concentrate on a particularly remarkable group which is called the Monster. The outcome of this investigation is likely to impact other areas of mathematics and physics.