一、题目

Erdös-Ko-Rado Type Theorems for Permutation Groups

二、主讲人

向青

三、摘要

The Erd{\H o}s-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.

四、主讲人简介

向青，南方科技大学讲席教授。研究领域包括组合设计、有限几何、编码理论和加法组合。1995年毕业于俄亥俄州立大学，获博士学位。1999年获得国际组合数学及其应用协会颁发的Kirkman奖章。曾任美国加州理工学院Bateman Instructor, 美国特拉华（Delaware）大学终身教职和浙江大学讲座教授。现为南方科技大学讲席教授。

五、邀请人

赵立璐 数学学院教授

六、时间

11月10日（周二）16:00-17:00

七、地点

腾讯会议 会议ID：460 732 686

八、主办方

山东大学数学学院