讲座主题：Group Extensions and Covers of Combinatorial Structures

专家姓名：杜少飞

工作单位：首都师范大学

讲座时间：2018年5月10日上午8:30-9:30

讲座地点：bob体育在线app数学与信息科学学院341

主办单位：bob体育在线app数学与信息科学学院

内容摘要：

Group extension theory is one of fundamental and important concepts in group theory and it is related to many branches of group theory. Generally, to determining a group extension is one of very difficult problem, although there exist some basic theories and methods, such as basic group extension theory, cohomology theory, Schur multiplier theory and representation theory and so on.

A cover X of a given (combinatorial, geometrical)-structure Y is an homomorphism \phi from X to Y, locally it is a bijection. A primitive idea for studying covers is that from a `small' structure with a given property P. We try to determine all the big `structures' so that such property P may be inherited. In many cases, we need a subgroup H in Aut(Y) to lift to a subgroup of Aut(X). Therefore, to class the covers is essentially a group extension problem. In this talk, 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.

主讲人介绍：

1996年获得北京大学博士学位，1998年到首都师范大学数学系工作,99年破格教授，02年担任博士生导师。杜少飞教授是代数组合领域的知名专家，很多工作深受国内外同行好评。到目前为止其主要学术贡献有：给出了半对称图的群论刻画，这样为近期将置换群和群与图方面的方法和结果用于半对称图的研究提供了有力的工具，进而完成了点数为2pq 的半对称图的分类；找到并证明了最小点数的本原半传递图；在给定基图为完全图，覆盖变换群为初等交换群Z_p^n的情况下做了尝试，分别完成了n=2,3的分类；给出了覆盖变换群为初等交换群的图的正则覆盖中自同构的提升的充要条件及线性算法；完成了二面体群2-弧传递Cayley图的分类；对于简单图的正则嵌入，通过用其自同构群来研究它，用陪集图来定义所谓的代数地图，从而为置换群理论在地图的分类中的应用提供了好的语言；给出了自同构群为单群PSL(3, p)的不可定向地图的分类等。到目前为止共主持了13项包括国家自然科学基金、教育部重点项目、国际合作项目等在内的科研课题。

讲座主题：Complete regular dessins and skew-morphisms of cyclic groups

专家姓名：胡侃

工作单位：浙江海洋大学

讲座时间：2018年5月10日上午9:30-10:30

讲座地点：bob体育在线app数学与信息科学学院341

主办单位：bob体育在线app数学与信息科学学院

内容摘要：

A dessin is a 2-cell embedding of a connected 2-colored bipartite graph into a closed orientable surface. A dessin is regular if its group of orientation- and color-preserving automorphisms acts transitively on the edges of the underlying bipartite graphs. On the other hand, a skew-morphism of a finite group A is a permutation \varphi on A fixing the identity element, and for which there exists an integer function \pi on A such that \varphi(xy)=\varphi(x)\varphi^{\pi(x)}(y) for all x,y\in A. In this talk I will show how regular dessins with complete bipartite underlying graphs are related to skew-morphisms of the cyclic groups.

主讲人介绍：

在斯洛伐克获得哲学博士，斯洛伐克科学院数学研究所博士后，现为浙江海洋大学副教授。研究方向有：群与图、群与地图、拓扑图论、涂鸦理论。