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理学院数理讲坛（2018年第33讲）

报告题目：Characterization of Intersecting Families of Maximum Size in PSL(2,q)

报告人： 向青  教授

单  位：University of Delaware

报告时间：2018年7月16日（星期一）9:00-10:00

报告地点：阳明学院303

报告摘要：

The Erdos-Ko-Rado (EKR) theorem is a classical result in extremal set theory. It states that when , any family of k-subsets of an n-set X, 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 X containing a fixed point.

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 , where q is an odd prime power. A subset S of PSL(2, q) is said to be an intersecting family if for any ,there exists an element  such that .It is known that the maximum size of an intersecting family in PSL(2, q) is .  We prove that all intersecting families of maximum size are cosets of point stabilizers for all odd prime powers .

报告人简介：

向青教授，现为美国特拉华(Delaware)大学教授、国家海外杰出青年科学基金获得者、国际组合数学及其应用协会Fellow。主要研究方向为组合数学，利用深刻的代数和数论工具来研究组合设计、有限几何、编码和加法组合中的问题。现为国际组合数学界权威SCI期刊《The Electronic Journal of Combinatorics》的主编，同时担任《Journal of Combinatorial Designs》、《Designs, Codes and Cryptography》、《Journal of Combinatorics and Number Theory》等SCI期刊的编委。曾被授予由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”。在国际组合数学高级别杂志《J. Combin. Theory Ser. A》、《Trans. Amer. Math. Soc.》、《IEEE Trans. Inform. Theory》等期刊上发表学术论文80余篇。主持完成美国国家自然科学基金、美国国家安全局科研项目等科研项目10余项。