本项目拟开展张量谱理论特别是一致超图谱问题的研究，同时开展超图谱在超图划分中的应用研究,拟综合运用分析不等式、非线性优化、张量代数以及超图结构分析等方法开展研究工作。具体研究内容如下: (1) 一致超图的 Normalized Laplace 张量与等周问题
：利用一致超图的 Normalized Laplace 张量，定义一簇相关参数。通过研究这些参数的性质，将图上的 Cheeger 不等式和分离不等式推广到一致超图上。(2) 无圈张量的谱性质研究，具体包括: 无圈张量的特征值与其匹配多项式的零点的关系；研究张量的匹配多项式与其子张量的匹配多项式的关系，以此来估计匹配多项式的零点的分布以及重数；将图上的 “Godsil-Gutman定理”推广到超图上。(3) 研究非负张量与其商张量的实特征值的交错问题。

The main goal of this project is the research on the spectrum theory of tensors, especially the uniform hypergraphs problem. Some applications of the spectrum of hypergraphs on hypergraph partitioning will be also studied. Analytic methods, nonlinear optimization methods, tensor theory, some combinatorial methods concerning structure of uniform hypergraphs will be comprehensively used in this project. The main content of this proposal contains the following. Firstly, the normalized Laplace tensors of uniform hypergraphs and isoperimetric inequalities: we first define a cluster of related parameters by means of the normalized Laplace tensors of uniform hypergraphs, and extend the Cheeger inequality and discrepancy inequality to uniform hypergraphs. Secondly, spectral properties of the acyclic tensors, including the relation between the eigenvalues of the acyclic tensors and the zero of the matching polynomial; the relation between the matching polynomials of tensors and their sub-tensors is studied. The "Godsil-Gutman theorem" on the graph is extended to the hypergraph. Thirdly, the problem of interlacing the real eigenvalues of the non-negative tensors and its quotient tensors is studied.