报告题目：Spectral radius of simplicial complexes with prescribed Betti number
时 间：2026年3月31日（星期二）10：30
地 点：理工南楼621
主 办：数学与统计学院，分析数学及应用教育部重点实验室，福建省分析数学及应用重点实验室
参加对象：相关专业师生
报告摘要：In this talk we investigate a spectral version of Turan problem for simplicial complexes. We characterize the simplicial complex that maximizes the signless Laplacian spectral radius among all hole-free simplicial complexes and establish an upper bound for the spectral radius of simplicial complexes with a prescribed Betti number. For 2-dimensional complexes with a prescribed second Betti number, we characterize the structure of the complexes attaining the maximum signless Laplacian spectral radius and determine the asymptotic value of this maximum. Moreover, for second Betti number equal to 1 or 2, we completely determine the corresponding extremal complexes. Our results extend classical extremal spectral results for graphs to the setting of simplicial complexes. As an application, we derive some bounds on Turan numbers for both hypergraphs and simplicial complexes via the connection between the spectral radius and the facet numbers.
报告人简介：范益政，安徽大学二级教授，博士生导师，教育部新世纪优秀人才，安徽省学术和技术带头人，中国数学会常务理事，中国运筹学会图论组合学分会理事，中国数学会组合数学与图论专业委员会委员，安徽省数学会副理事长，安徽省工业与应用数学学会副理事长。研究领域为代数图论和代数组合，主持1项国家自然科学基金重点项目，完成4项国家自然科学基金项目，在Tran AMS, Proc AMS, J Combin Theory Ser A等期刊发文120余篇。