报告题目：On local Tur\'an density problems of hypergraphs

报告人：方春秋，东莞理工学院

报告时间：2024年1月19日（周五）10:00-11:00

报告地点：21-411

报告摘要：For integers q \geq p \geq r \geq 2, we say that an r-uniform hypergraph H has property (q, p), if for any q-vertex subset Q of V(H), there exists a p-vertex subset P of Q spanning a clique in H. Let T_{r}(n, q, p)=\min\{e(H): H \subset \binom{[n]}{r}, H has property (q,p)\}. The local Tur\'an density about property (q, p) in r-uniform hypergraphs is defined as t_{r}(q, p) = \lim_{n \to \infty} T_{r}(n, q, p)/ \binom{n}{r}. Frankl, Huang and R\odl [J. Comb. Theory, Ser. A, 177 (2021)] showed that \lim_{p \to \infty} t_{r}(ap+1, p+1) = \frac{1}{a^{r-1}} for positive integer a and t_{3}(2p+1, p+1)=\frac{1}{4} for all p \geq 3 and asked the question that determining the value of \lim_{p \to \infty} t_{r}(\gamma p+1, p+1), where \gamma \geq 1 is a real number. In this talk, I will present some recent results on this problem.  Joint work with Guorong Gao, Jie Ma and Ge Song.

报告人简介：方春秋，东莞理工学院讲师。2020年获清华大学理学博士学位，博士期间曾于匈牙利Alfréd Rény研究所公派访问一年，中国科学技术大学博士后。主要从事Anti-Ramsey, Turan数等极值组合问题的研究。目前在 J. Combin. Des. 、 Electron. J. Combin. 等杂志发表学术论文7篇，主持国家自然科学基金青年基金一项。

邀请人：徐荣兴