报告题目: Characterization of Intersecting Families of Maximum Size in PSL(2, q)
报告人: Prof. Qing Xiang (向青) (University of Delaware)
时间：2018年7月26日下午16：00-17：00
地点：维格堂319
报告摘要
The Erdős-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,; 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 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 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. (Joint work with Ling Long, Rafael Plaza, and Peter Sin)
报告人简介
向青博士现为美国特拉华大学教授、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，擅长于使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。美国Math. Reviews对他的工作评论认为“的确非常优美”（indeed very elegant）。现为国际组合数学界权威SCI期刊《The Electronic Journal of Combinatorics》主编，同时担任SCI期刊《Journal of Combinatorial Designs》、《Designs, Codes and Cryptography》、《Journal of Combinatorics and Number Theory》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”。