范益政教授学术报告

报告题目：The eigenvectors of nonnegative tensors and hypergraphs associated with spectral radius

报告人: 范益政 教授 （安徽大学）

报告时间: 2019年8月6日上午9:00

报告地点: 数学院大会议室

内容摘要：In this talk we showed that such projective eigenvariety admits a module structure, which is determined by the support of the tensor and can be characterized explicitly by the Smith normal form of the incidence matrix of the tensor. We introduced two parameters: the stabilizing index and the stabilizing dimension of the tensor, where the former is exactly the cardinality of the projective eigenvariety and the latter is the composition length of the projective eigenvariety as a module. We give some upper bounds for the two parameters, and characterize the case that there is only one eigenvector of the tensor corresponding to the spectral radius, i.e. the Perron vector. By applying the above results to the adjacency tensor of a connected uniform hypergraph, we give some upper bounds for the two parameters in terms of the structural parameters of the hypergraph such as path cover number, matching number and the maximum length of paths.

报告人简介: 范益政，男，教授，博士，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，中国工业与应用数学学会图论组合及应用专业委员会副主任委员，中国运筹学会图论组合学分会常务理事，中国数学会图论与组合专业委员会委员，安徽省数学会常务理事，安徽大学数学科学学院院长。主要研究方向：代数组合与谱图理论。主持国家自然科学基金项目4项，发表论文100余篇。