讲座主题：Strong counterexamples to Mubayi＇s supersaturation conjecture

专家姓名：王婧

工作单位：河南师范大学

讲座时间：2026年09月18日 19:00-21:00

讲座地点：腾讯会议：793-198-062

主办单位：烟台大学数学与信息科学学院

内容摘要：

The supersaturation problem asks, for a fixed r-graph F, for the minimum number of copies of F in an n-vertex r-graph with ex(n, F) + q edges. Mubayi conjectured a local form of supersaturation under a stability hypothesis: if F is non-r-partite and stable, meaning roughly that the extremal F-free construction is unique and all near-extremal F-free r-graphs are close to it, then this minimum should be at least q c(n, F), where c(n, F) is the minimum number of copies created by adding one edge to the extremal F-free r-graph. We disprove this conjectured local lower bound in the strongest possible quantitative sense that the ratio to the conjectured lower bound can be made arbitrarily small. More precisely, for every r ≥ 2 and every K ＞ 1, we construct a stable non-r-partite r-graph F and a constant δ ＞ 0 such that, for all sufficiently large n and every integer q with 1 ≤ q ≤ δn, there is an n-vertex r-graph with ex(n, F) + q edges containing at most K⁻¹ q c(n, F) copies of F. This arbitrarily large failure already occurs when q = 1. This is joint work with Heng Li, Hong Liu and Xizhi Liu.

主讲人介绍：

王婧，河南师范大学副研究员、硕士生导师。在JCTB、DM、EJC、LAA 等期刊发表 SCI 论文多篇。主持国家自然科学基金青年项目 1 项、中国博士后科学基金项目 1 项、河南省青年人才托举工程项目 1 项。2025 年 9 月至 2026 年 9 月赴韩国基础科学研究院访问刘鸿教授。