The algebraic structures of group rings and related topics

环是满足某些公理的代数系统。交换环K上群G的群环是所有形式有限和的环KG，是一个有吸引力的研究对象。在这里，群论、环论、交换代数和数论以一种富有成效的方式结合在一起。我最近的研究工作揭示了群环及其单位群的代数结构，并在编码理论和组合数论中有重要的应用。这将是我未来5年的研究方向。我将研究群环中的几个开放问题和猜想，包括规范化问题——一个长期存在的研究问题，以及第一个Zassenhaus猜想。虽然我最近的大部分工作都是在群环中，但我也参与了其他一些领域，包括模块理论。最近，我开始研究一个新的令人兴奋的领域。高博士和我能够使用群环作为工具来研究组合数论中的一些问题，如达文波特常数和更一般的零和问题。

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.