报告题目：Unit gain graphs with two eigenvalues and lines in complex space with few angles
报告人：Edwin van Dam
地点：第四教学楼 215教室
摘要：Since the introduction of the Hermitian adjacency matrix for digraphs, interest in so-called complex unit gain graphs has surged. In this talk, we consider such gain graphs with two distinct eigenvalues. Analogously to (undirected) graphs whose traditional adjacency matrix has few distinct eigenvalues, a great deal of structural symmetry is required. Besides combinatorial considerations, also the representation by lines in complex space is essential in the study of considered gain graphs. Examples are drawn from various relevant concepts from quantum information theory related to lines in complex space with few angles, such as SIC-POVMs and MUBs. Other examples relate to the hexacode, Coxeter-Todd lattice, and the Van Lint-Schrijver association scheme. Many other examples can be obtained as induced subgraphs by employing a technique parallel to the dismantling of certain association schemes. Specific examples thus arise from (partial) spreads in some small generalized quadrangles. Finally, we give a full classification of two-eigenvalue gain graphs with degree at most 4, or with a multiplicity at most 3.
报告人简介：
Edwin R. van Dam is currently a Full Professor in the Department of Econometrics and Operations Research at Tilburg University, the Netherlands. He obtained his Ph.D. from Tilburg University.
His main research interests include algebraic graph theory, spectral graph theory, distance-regular graphs, association schemes, and the use of eigenvalue methods in combinatorics. Professor van Dam has published over 100 papers in highly prestigious journals such as Inventiones Mathematicae, Journal of Combinatorial Theory Series A, Journal of Combinatorial Theory Series B. He is an Editor-in-Chief of the Electronic Journal of Combinatorics.
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