The algebraic structures of group rings and related topics

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A ring is an algebraic system satisfying  certain axioms. The group ring of a group G over a commutative ring K is the ring KG of all formal finite sums, and is an attractive object of study. Here group theory, ring theory, commutative algebra and number theory come together in a fruitful way.My recent research work has thrown light on the algebraic structures of group rings and their unit groups, and has important applications in coding theory and combinatorial number theory. This will continue to be the main stream of my research program for the next 5 years. I will study several open problems and conjectures in group rings, including  the normalizer problem -- a long standing research problem, and the first Zassenhaus Conjecture. While much of my recent work is in group rings, I am also involved in some other areas including module theory. Most recently, I have started research in a new exciting area. Dr. Gao and I are able to use group rings as a tool to investigate some problems in combinatorial number theory such as Davenport's constant and the more general zero-sum problems.