Seminars on Discrete Mathematics：Digraphs with non-diagonalizable adjacency matrix

：夏彬绉（墨尔本大学）
：2022-11-16 15:00
：腾讯会议ID：755-059-3114（无密码）

报告人：夏彬绉（墨尔本大学）

时  间：11月16日下午15:00-16:30

地  点：腾讯会议ID：755-059-3114（无密码）

内容摘要:

The fact that the adjacency matrix of every finite graph is diagonalizable plays a fundamental role in spectral graph theory. Since this fact does not hold in general for digraphs, it is natural to ask whether it holds for digraphs with certain level of symmetry. Interest on this question dates back to early 1980s, when P. J. Cameron asked for the existence of arc-transitive digraphs with non-diagonalizable adjacency matrix. This was answered in the affirmative by L. Babai in 1985. Then Babai posed the open problem of constructing a 2-arc-transitive digraph and a vertex-primitive digraph whose adjacency matrices are not diagonalizable. In this talk, we will give a solution to Babai's problem by constructing an infinite family of 2-arc-transitive digraphs and of vertex-primitive digraphs, respectively, both of whose adjacency matrices are non-diagonalizable.

This talk is based on joint work with Yuxuan Li, Sanming Zhou and Wenying Zhu.

个人简介：

夏彬绉博士现就职于澳大利亚墨尔本大学。他于2014年获得北京大学博士学位，2014-2016年在北京国际数学研究中心从事博士后研究，2016-2017年西澳大利亚大学Research Associate。曾获得国际组合数学与应用学会(ICA) 2017年度的Kirkman奖章。其主要研究方向为代数图论、组合学与群论。在诸多国际杂志（如《Mem. Amer. Math. Soc.》、《Israel J. Math》、《J. Combin. Theory Ser. A/B》等）发表了多篇文章。

 

联系人：陈继勇