报告人：鲁红亮 教授
报告题目：Towards the Erd\H{o}s matching conjecture for 4-uniform hypergraphs: stability and applications
报告时间：2026年5月20日（周三）下午7：30
报告地点：腾讯会议：907-381-1970
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
鲁红亮，西安交通大学教授，博士生导师，研究方向组合最优化和极值图论，主持多项国家基金项目，发表论文百余篇。获邀第十三届海峡两岸图论与组合数学大会报告（2025）、国际基础科学大会邀请报告(ICBS)（2023）、华人数学家大会邀请报告(ICCM)（2022）等国际重要大会报告。荣获第十三届陕西青年科技奖（2020），入选国家级青年人才项目---四青人才计划（2019），中国运筹学会图论与组合分会青年论文奖一等奖（2017）等。
报告摘要：
A famous conjecture of Erd\H{o}s asserts that for $k\ge 3$, the maximum number of edges in an $n$-vertex $k$-uniform hypergraph without $s+1$ pairwise disjoint edges is $\max\{\binom{n}{k}-\binom{n-s}{k},\binom{sk+k-1}{k}\}$.This problem has been central in extremal combinatorics, with substantial progress in the literature, including a complete solution for $k=3$ due to the first author.
In this paper, we make progress towards the $4$-uniform case, proving the conjecture for $n\ge 5s$ and sufficiently large $n$, thereby taking a first step analogous to the $3$-uniform case. The main technical contribution is a stability result of independent interest. We further apply this stability to resolve two new instances of conjectures on the minimum $d$-degree threshold for matchings in $5$- and $6$-uniform hypergraphs, in a strengthened form. This is joint work with Frankl, Ma, and Wu.