会议时间：2024年10月20日18：00-19：40
会议地点：线下地点（科研实验大楼B104），
线上地点（腾讯会议室 640 912 476，无密码）
报告题目：Laplacian eigenvalue distribution and diameter of graphs
报告时间：2024年10月20日18：20-19：00
报告人：周波 (Bo Zhou) 教授 （华南师范大学数学科学学院）
报告摘要:
Any Laplacian eigenvalue of an n-vertex simple graph lie in [0,n]. The distribution of Laplacian
eigenvalues of graphs is relevant to the many applications related to Laplacian matrices. Little is known about how the Laplacian eigenvalues are distributed in the interval [0, n]. For a graph G and an interval I, denote by m_GI the number of Laplacian eigenvalues of G in I. We discuss results relating m_GI for some subinterval I of [0, n] to the diameter of (connected) graphs G.
报告人简介：周波，华南师范大学数学科学学院，教授,博士生导师。主要兴趣包括组合矩阵论、代数图论及数学化学。近年来主要工作在图与超图谱理论方面。主持过多项国家及广东省自然科学基金项目的研究。
报告题目：Tur\'{a}n problems on graph-based hypergraphs
报告时间：2024年10月20日19：00-19：40
报告人：袁西英 （Xiying Yuan）教授 （上海大学数学系）
报告摘要：For a graph $F$, a hypergraph $H$ is a Berge-$F$ if there is a bijection $\phi:E(F)\rightarrow E(H)$ such that $e\subseteq \phi(e)$ for each $e\in E(F)$. The $r$-expansion of $F$ is the $r$-graph $F^r$ obtained from $F$ by inserting $r-2$ new distinct vertices in each edge of $F$. Given a family $\mathcal{F}$ of hypergraphs, a hypergraph $H$ is $\mathcal{F}$-free if $H$ does not contain any member in $\mathcal{F}$ as a subhypergraph. The Tur\'{a}n number of $\mathcal{F}$ is the maximum number of hyperedges in an $\mathcal{F}$-free $r$-graph on $n$ vertices.
Our work focuses on studying the Tur\'{a}n problems on graph-based hypergraphs. Specifically, some stability results for Berge-$K_{s,t}$ linear $r$-graphs are obtained. As applications, the upper bounds for linear Tur\'{a}n number of Berge-$K_{2,t}$ and Berge-$K_{3,t}$ are determined. For expansions, an upper bound for the linear Tur\'{a}n number of $P_\ell^r$ is obtained, and some results for the linear Tur\'{a}n number and Tur\'{a}n number of some linear star-path forests are obtained. Moreover, some results for the linear Tur\'{a}n number of expansion of graphs with bounded matching number are obtained.
报告人简介：袁西英，上海大学数学系教授，博士生导师。主要从事图谱理论和极值图论的研究。先后主持四项国家自然基金项目。曾访问美国孟菲斯大学、威廉玛丽学院以及日本东北大学，曾多次赴香港理工大学应用数学系，开展合作研究。