A Linear Analogue of Kneser's Theorem in Additive Combinatorics and Related Problems
科研大讨论系列报告
报告题目(Title)：A Linear Analogue of Kneser's Theorem in Additive Combinatorics and Related Problems
报告人(Speaker)：向青 教授 （南方科技大学）
地点(Place)：后主楼 1124
时间(Time)：2023 年 9 月 15 日（周五） 16:00--17:00
邀请人(Inviter)：吕本建、王恺顺
报告摘要
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∣a∈A,b∈B\} then |AB|≥|A|+|B|-|H(AB)|, where H(AB)=\{g∣g∈G,g(AB)=AB\}. More than a decade 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.
主讲人简介
向青，现为南方科技大学数学系主任、讲席教授。向青教授于1995获美国 Ohio State University博士学位。主要研究方向为组合设计、有限几何、编码理论和加法组合。在国际组合数学界最高级别杂志《J. Combin. Theory Ser. A》，《J. Combin. Theory Ser. B》，《Combinatorica》, 以及顶尖的数学综合期刊《Advances in Math.》，《Trans. Amer. Math. Soc.》等重要国际期刊上发表学术论文98篇。主持完成美国国家自然科学基金、中国国家自然科学基金海外及港澳学者合作研究基金等科研项目10余项。正在主持中国国家自然科学基金重点项目一项，以及海外资深研究学者基金一项。曾在国际学术会议上作大会报告或特邀报告60余次。
