Mathematical Sciences: Group Theory and Combinatorics

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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.