报告题目：On the improved Brouwer's Laplacian spectrum conjecture
报 告 人：郭继明（华东理工大学数学学院 教授）
报告时间：2021年11月19日 上午9:30开始
报告地点：腾讯会议线上报告
会议链接：//meeting.tencent.com/dm/hvP2lXiZWLNu
会议ID：319 464 181
报告摘要：Let $G$ be a simple connected graph with $n$ vertices. The matrix $L(G)=D(G)-A(G)$ is called Laplacian matrix of $G$, where $A(G)$ is the adjacency matrix of $G$ and $D(G)=diag(d(v_1),d(v_2),\ldots,d(v_n))$ is the diagonal matrix of vertex degrees of $G$.It is well known that $L(G)$ is a positive semidefinite and symmetric real matrix.Let $S_k(G)$ be the sum of the first $k$ largest Laplacian eigenvalues of $G$.
It was conjectured by Brouwer that $S_k(G)\leq e(G)+\binom{k+1}{2}$ holds for $1\leq k\leq n-1$. In this topic,we propose the improved Brouwer's Laplacian spectrum conjecture and prove the conjecture holds for $k=2$ which also confirm the conjecture of Guan et al. in 2014.
报告人简介：郭继明，华东理工大学数学学院教授、博士生导师。中国高等教育学会教育数学专业委员会常务理事、上海市数学会常务理事、中国工业与应用数学学会理事。主要研究方向为图论与组合数学，先后主持多项国家自然科学基金面上项目，在国内外杂志上发表论文80余篇、出版学术专著一部。
