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向青教授学术报告

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主讲人:向青教授  

报告时间:2020年7月10日10:00

报告地点:腾讯会议  ID:357 105 926

报告题目:Erdos-Ko-Rado  Type Theorems for Permutation Groups

报告摘要:The  Erdos-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, …, 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, …, 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 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.

个人简介:向青,1995获美国  Ohio State University博士学位。向青教授的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《Journal of Combinatorial  Designs》、《Designs, Codes and  Cryptography》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》,以及《Trans. Amer. Math.  Soc.》,《IEEE Trans. Inform.  Theory》等重要国际期刊上发表学术论文90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。