报告题目：Connectivity of $p$-subgroup posets with irreducible characters

报告人：孟沆洋（上海大学 副教授）

报告时间：2026年1月4日（星期日） 下午16:00-17:00

地点：明理楼401

报告摘要：

Let $G$ be a finite group. For a prime $p$ and an integer $e \geq 0$, we denote by $\Gamma_{p,e}(G)$ the set of all pairs $(H, \varphi)$, where $H$ is a $p$-subgroup of $G$ of order greater than $p^e$ and $\varphi$ is a complex irreducible character of $H$. In this talk, we will introduce the connected components of the poset $\Gamma_{p,e}(G)$. For the case $e = 0$, we prove that $\Gamma_{p,0}(G)$ is disconnected if and only if either $G$ has a strongly $p$-embedded subgroup, or every Sylow $p$-subgroup of $G$ contains a unique subgroup of order $p$. Furthermore, for $e = 1$ and $G$ a $p$-group, we show that the number of connected components of $\Gamma_{p,1}(G)$ equals the order of the intersection of all subgroups of $G$ of order $p^2$.

报告人简介：

孟沆洋，上海大学理学院数学系副教授，西班牙瓦伦西亚大学基础数学博士，主要研究领域为有限群论及其表示、量子Yang-Baxter方程解与Braces。相关结果发表于Trans. Amer. Math. Soc., J. Lond. Math. Soc.，J. Algebra等杂志。 获上海市2020年度扬帆计划、2020年度上海市引智人才XSC计划，2021年获 Baer Prize特别提名奖，主持国家自然科学基金青年项目一项，面上项目一项。