報告題目：Erd?s-Ko-Rado Type Theorems for Permutation Groups
(置換群的 Erd?s-Ko-Rado 定理)
主講人：向青 教授
時間：2020年6月30日（周二）10:00 a.m.
地點：北院卓遠(yuǎn)樓305會議室
主辦單位：統(tǒng)計與數(shù)學(xué)學(xué)院
摘要：The Erd?s-Ko-Rado (EKR) theorem is a classical result in extremal set theory. It states that when $k
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 {/it 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.
主講人簡介：向青，1995年獲美國俄亥俄州立大學(xué)博士學(xué)位。向青教授的主要研究方向為組合設(shè)計、有限幾何、編碼和加法組合。現(xiàn)為國際組合數(shù)學(xué)界權(quán)威期刊《The Electronic Journal of Combinatorics》主編，同時擔(dān)任SCI期刊《Journal of Combinatorial Designs》、《Designs, Codes and Cryptography》的編委。曾獲得國際組合數(shù)學(xué)及其應(yīng)用協(xié)會頒發(fā)的杰出青年學(xué)術(shù)成就獎—Kirkman Medal。在國際組合數(shù)學(xué)界最高級別雜志《J. Combin. Theory Ser. A》，《J. Combin. Theory Ser. B》, 以及《Trans. Amer. Math. Soc.》，《IEEE Trans. Inform. Theory》等重要國際期刊上發(fā)表學(xué)術(shù)論文90余篇。主持完成美國國家自然科學(xué)基金、美國國家安全局等科研項目10余項。在國際學(xué)術(shù)會議上作大會報告或特邀報告50余次。
滇公網(wǎng)安備53010202000350號滇ICP備17008047號 Copyright ? 2013 Yunnan University of Finance and Economics All Rights Reserved
