报告题目：Generating non-jumps from a known one

报 告 人：侯建锋，福州大学

报告摘要：Let $r\geq 1$ be an integer. The real number $\alpha \in [0, 1]$ is a jump for $r$ if there exists a constant $c > 0$ such that for any $\epsilon > 0$ and any integer $m\geq r$, there exists an integer $n_0(\epsilon, m)$ satisfying any $r$-uniform graph with $n\geq n_0(\epsilon, m)$ vertices and density at least $\alpha+\epsilon$ contains a subgraph with $m$ vertices and density at least $\alpha + c$. A result of Erd\H{o}s, Stone and Simonovits implies that every $\alpha \in [0, 1)$ is a jump for $r = 2$. Erd\H{o}s asked whether the same is true for $r\geq 3$. Frankl and R\"odl gave a negative answer by showing that $1-\frac{1}{l^{r-1}}$ is not a jump for $r$ if $r\geq 3$ and $l > 2r$. After that, more non-jumps are found using a method of Frankl and R\"odl. Motivated by an idea of Liu and Pikhurko, in this talk we show a method to construct maps $f : [0, 1]\rightarrow [0, 1]$ that preserve non-jumps, i.e., if $\alpha$ is a non-jump for $r$ given by the method of Frankl and R\"odl, then $f(\alpha)$ is also a non-jump for $r$. We use these maps to study hypergraph Tur\'an densities and answer a question posed by Grosu. (Join work with Heng Li, Caihong Yang and Yixiao Zhang).

报告人简介：侯建锋，福州大学教授，博士生导师。2009年7月毕业于山东大学数学学院，获理学博士学位。2011年度全国优秀博士学位论文提名奖，2011年度福建省自然科学基金杰出青年项目获得者，2020年入选福建省“雏鹰计划”青年拔尖人次，2021年入选青年长江学者计划，主持国家自然科学基金4项，参与重点项目一项，主要从事图论及其应用研究，发表论文60余篇。中国数学会组合数学与图论专业委员会委员，中国工业与应用数学学会图论组合及应用专业委员会委员，福建省数学会常务理事，美国数学评论“Mathematical Review”评论员。

报告时间：2022年11月17日14:30-16:30

报告地点：腾讯会议ID：892330398

主办单位：伟德国际1946源自英国