講座主題：The eigenvectors of nonnegative tensors and hypergraphs associated with spectral radius
主講人： 范益政
工作單位：安徽大學(xué)
講座時(shí)間：2019年8月6日9:00
講座地點(diǎn)：數(shù)學(xué)院大會(huì)議室
主辦單位：煙臺大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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.
主講人介紹：
范益政，男，教授，博士，博士生導(dǎo)師，教育部新世紀(jì)優(yōu)秀人才，安徽省學(xué)術(shù)和技術(shù)帶頭人，中國工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)圖論組合及應(yīng)用專業(yè)委員會(huì)副主任委員，中國運(yùn)籌學(xué)會(huì)圖論組合學(xué)分會(huì)常務(wù)理事，中國數(shù)學(xué)會(huì)圖論與組合專業(yè)委員會(huì)委員，安徽省數(shù)學(xué)會(huì)常務(wù)理事，安徽大學(xué)數(shù)學(xué)科學(xué)學(xué)院院長。主要研究方向：代數(shù)組合與譜圖理論。主持國家自然科學(xué)基金項(xiàng)目4項(xiàng)，發(fā)表論文100余篇。
