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【6月30日】数学学术讲座

】【打印】【关闭窗口 来源:本站原创 作者:统计与数学学院 编辑:张薇 发布时间:2020-06-29
       报告题目:Erdős-Ko-Rado Type Theorems for Permutation Groups 
                     (置换群的 Erdős-Ko-Rado 定理)
       主讲人:向青 教授
       时间:2020年6月30日(周二)10:00 a.m.
       地点:北院卓远楼305会议室
       主办单位:统计与数学学院

       摘要:The Erdős-Ko-Rado (EKR) theorem is a classical result in extremal set theory. It states that when $k<n/2$, any family of $k$-subsets of $/{1,2,/ldots ,n/}$, with the property that any two subsets in the family have nonempty intersection, has size at most ${n-1/choose k-1}$; equality holds if and only if the family consists of all $k$-subsets of $/{1,2,/ldots ,n/}$ containing a fixed element.
       Here we consider EKR type problems for permutation groups. In particular, we focus on the action of the $2$-dimensional projective special linear group $PSL(2,q)$ on the projective line $PG(1,q)$ over the finite field ${/mathbb F}_q$, where $q$ is an odd prime power. A subset $S$ of $PSL(2,q)$ is said to be an {/it intersecting family} if for any $g_1,g_2 /in S$, there exists an element $x/in PG(1,q)$ such that $x^{g_1}= x^{g_2}$. It is known that the maximum size of an intersecting family in $PSL(2,q)$ is $q(q-1)/2$. We prove that all intersecting families of maximum size must be cosets of point stabilizers for all odd prime powers $q>3$. This talk is based on joint work with Ling Long, Rafael Plaza, and Peter Sin.

       主讲人简介:向青,1995年获美国
俄亥俄州立大学博士学位。向青教授的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90余篇。主持完成美国国家自然科学基金、美国国家安全局等科研项目10余项。在国际学术会议上作大会报告或特邀报告50余次。
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