91直播

91直播：夏彬绉 高级讲师（澳大利亚墨尔本大学）

时间：2024年11月26日 15:00-

地点: 理科楼LA103

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.

邀请人: 傅士硕

欢迎广大师生积极参与！