A linear Analogue of Kneser's Theorem and Related Problems

报告题目: A linear Analogue of Kneser's Theorem and Related Problems

报  告 人: Prof. Qing Xiang  

报告时间: 11月28日(周二)    上午10:00

报告地点: 学院办公楼205


A theorem of Kneser in additive combinatorics states that in an abelian group $G$ if $A$ and $B$ are finite subsets in $G$ and $AB=\{ab\mid a\in A, b\in B\}$ then $|AB|\geq |A|+|B|-|H(AB)|$, where $H(AB)=\{g\mid g\in G, g(AB)=AB\}$. More than fifteen years ago, motivated by the study of a problem about finite fields, we (jointly with Xiang-Dong Hou and Ka Hin Leung) proved an analogous result for vector spaces over a field $E$ in an extension field $K$ of $E$, which is now called a linear analogue of Kneser's theorem. This linear analogue has found some interesting applications and motivated further investigations. We will talk about this linear analogue of Kneser's theorem and related problems.


向青,1995获美国 Ohio State University博士学位, 现为美国特拉华大学(University of Delaware)教授。主要研究方向为组合设计、有限几何、编码和加法组合。现为国际组合数学界权威期刊《The Electronic Journal of Combinatorics》主编,同时担任SCI期刊《Journal of Combinatorial Designs》、《Designs, Codes and Cryptography》的编委。曾获得国际组合数学及其应用协会颁发的杰出青年学术成就奖—Kirkman Medal。在国际组合数学界最高级别杂志《J. Combin. Theory Ser. A》,《J. Combin. Theory Ser. B》, 以及《Trans. Amer. Math. Soc.》,《IEEE Trans. Inform. Theory》等重要国际期刊上发表学术论文80余篇。主持完成美国国家自然科学基金、美国国家安全局科研项目等科研项目10余项。曾在国际学术会议上作大会报告或特邀报告50余次。