深圳大学四十周年校庆暨数学学科四十周年庆

荔园学者Colloquium第四十四期

讲座题目: Erds-Ko-Rado Type Theorems for Permutation Groups

主讲人：向青教授（南方科技大学）

讲座时间：2023年10月17日下午16:30-17:30

讲座地点：深圳大学粤海校区汇星楼M1号教室

内容概述：

The Erds-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 [n] := {1,2,...,n}, with the property that any two subsets in the family have nonempty intersection, has size at most;equality holds if and only if the family consists of all k-subsets of [n] containing a fixed element.

Here we consider EKR type problems for permutation groups. In par- ticular, 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 where q is an odd prime power. A subset S of PSL(2,q) is said to be an intersecting family if for any g1,g2 ∈ S, there exists an element x ∈ PG(1,q) such that xg1 = xg2 . It is known that the maximum size of an intersecting family in P SL(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，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99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。

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数学科学学院

2023年10月15日