全校师生：

我校定于2020年12月12日举办研究生灵犀学术殿堂——马杰教授报告会，现将有关事项通知如下：

一、报告会简介

报告人：马杰 教授

时 间：2020年12月12日（星期六）10:00

地点：腾讯会议(会议号381465733)

报告题目：Minimizing cycles in tournaments and normalized q-norms

内容简介：Akin to the Erdös-Rademacher problem, Linial and Morgenstern made the following conjecture in tournaments: for any d∈(0,1], among all n-vertex tournaments with dCn3 many 3-cycles, the number of 4-cycles is asymptotically minimized by a special random blow-up of a transitive tournament. Recently, Chan, Grzesik, Král' and Noel introduced spectrum analysis of adjacency matrices of tournaments in this study, and confirmed this for d≥1/36.

In this paper, we investigate the analogous problem of minimizing the number of cycles of a given length. We prove that for integers l≠2(mod 4), there exists some constant cl>0 such that if d≥1-cl, then the number of l-cycles is also asymptotically minimized by the same extremal examples. In doing so, we answer a question of Linial and Morgenstern about minimizing the q-norm of a probabilistic vector with given p-norm for integers q>p>1. For integers l≡2(mod 4), however the same phenomena do not hold for l-cycles, for which we can construct an explicit family of tournaments containing fewer l-cycles for any given number of 3-cycles. We propose two conjectures concerning the minimization problem for general cycles.

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党委学生工作部

数学与统计学院

2020年12月7日

报告人简介

    马杰，中国科学技术大学数学科学学院教授，博士生导师。研究领域为极值组合、图论、概率组合，以及在计算机科学和优化问题方面的应用研究。2017年获国家优秀青年科学基金项目资助，2018年开始担任SIAM离散数学杂志编委。