题  目：Characterization of Intersecting Families of Maximum Size in PSL(2; q)

报告人：向 青    教 授     (美国Delaware大学数学系)

摘  要：The Erdös-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 an n-set X, with the property that any two subsets in the family have nonempty intersection, has size at most binom(n-1,k-1); 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 Fq, where q is an odd prime power. A subset S of PSL(2; q) is said to be an intersecting family if for any g, h∈ S, there exists an element x ∈ PG(1; q) such that xg = xh . 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 are cosets of point stabilizers for all odd prime powers q > 3.

时  间: 2018年4月27日（星期五） 上午 10:00—11:00

地  点:  数学系西大楼三楼报告厅308室

报告人简介：

向青，1995获美国 Ohio State University博士学位, 现为美国特拉华大学(University of Delaware)教授。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《Designs, Codes and Cryptography》, 《Journal of Combinatorial Designs》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》,  《Combinatorica》,以及《Trans. Amer. Math. Soc.》,《IEEE Trans. Inform. Theory》等重要国际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、美国国家安全局等科研项目10余项。曾在国际学术会议上作大会报告或特邀报告50余次。

邀请人: 孙智伟 老师