【学术讲座】-Johannes Siemons教授-Construction of graphs with singular adjacency matrix

2019年04月15日 09:21  


报告题目:Construction of graphs with singular adjacency matrix

:Johannes Siemons教授

邀请:刘晓刚副教授

报告时间:2019年4月19日(星期五)下午14:30-15:30

报告地点:长安校区理学院214会议室

报告简介:Let Γbe a finite undirected graph without loops or multiple edges. Then Γ issingularif its adjacencymatrixissingular.Alternatively, Γissingularifandonlyif itsadjacencyspectrum contains the eigenvalue0.Singular graphs play a significant role in physics and chemistry(e.g. HückelTheory),but have also ramifications for problems in algebra, combinatorics and incidence geometries.Westartwithan introductory remarks on graph singularity, explainingits significanceandbasic asymptotic behaviour, including the work ofT. Tao,Van Vu, K.Costello and E. Szemerédi.While a great deal is known about graph spectra--so that singularity could be decided just by looking up a data base--it is not likely that a general theory of graph singularityper sewill emerge.Some progress however can be made for graphs which have a groupGof automorphismsthat acts transitively on the vertices of the graph.Here the singularity question can be discussed, in some cases,via the linear representation theory ofG.It turn out that singularity is closely related to the vanishing of certain characters ofG.In the second part of the lecture I will discuss connections between graph spectra and automorphism groups. The details can be found in a recent paper[1] with A. Zaleski.

References

[1]J. SiemonsandA. Zaleskii,Remarks on singular Cayley graphs and vanishing elements of simple groups,J.Algebraic Combinatorics,2018.

报告人简介:Johannes Siemons,东安格利亚大学(University of East Anglia)数学学院教授,1976年获德国海德堡大学数学物理学士学位,1979年获英国伦敦帝国理工学院博士学位。Journal of Combinatorial Designs期刊编委(2006-至今),上海组合学国际会议学术委员会委员(2014-至今)。研究领域涉及代数、组合、设计、图论、有限几何、有限置换群及其应用等。在Journal of Algebra、Journal of Combinatorial Theory Ser A、Journal of Algebraic Combinatorics、Designs, Codes and Cryptography、European Journal of Combinatorics等期刊上发表学术论文70余篇,被引500余次。长期主讲代数(Algebra)、几何(Geometry)、群论(Group Theory)、图论(Graph Theory)、组合(Combinatorics)等课程,精于从概念本质启发、引导学生,教法独特,效果优异。

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