题目：Arc-Transitive Covers of Graphs

主讲人：杜少飞 (教授)

时间：2025年6月27日（星期五）16:00

地点：理学院310

主办单位：理学院

主讲人简介：

杜少飞，首都师范大学教授。1996年在北京大学数学系获得博士学位，师从徐明曜教授学习有限群论和代数组合论。1998年来首都师范大学数学系工作，1999年6月评为教授，2002年6月担任博士生导师。他的研究方向有限群论以及图、地图等组合结构的对称性研究。近30年来，他在半对称图、图的正则覆盖、正则地图理论及点传递图的Hamilton圈方面做了大量研究工作。 在Journal of Combinatorial Theory A及B,  Combinatorica,  Journal of Algebra等专业领域的权威杂志上发表论文近70篇，其博士论文在MathSciNet上被引用76次。他和国际同行有着广泛的长期合作，曾30次出国交流与合作，担任国际期刊Journal of Algebraic Combinatorics (SCI)和Ars Mathematica Contemporanea (SCI)的编委。曾主持国家基金面上项目6项。

摘要：

  A cover $X$ of a given graph $Y$ is an homomorphism $\phi $ from $X$ to $Y$, locally it is a bijection. This is one of fundamental and important concepts in    topological graph theory.  Another motivation for us to study covers might be from  classifications of finite arc-transitive graphs, mainly 2-arc-transitive graphs. In this talk, I shall show that why we study covers, how to construct covers, what is the advantages of covering graphs, comparing with other representations of graphs (for instance, coset graphs), and how to recognize the symmetric properties from the covers. In particular, by exhibiting some examples I try to show you the relationships between   construction of covers and group extension theory, group representation theory and  topological graph theory.