报告题目：Erd?s-Ko-Rado Type Theorems for Permutation Groups
(置换群的 Erd?s-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 Erd?s-Ko-Rado (EKR) theorem is a classical result in extremal set theory. It states that when $k
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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