講座主題：Group Extensions and Covers of Combinatorial Structures
專家姓名：杜少飛
工作單位：首都師范大學(xué)
講座時間：2018年5月10日上午8:30-9:30
講座地點(diǎn)：煙臺大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院341
主辦單位：煙臺大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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.
主講人介紹：
1996年獲得北京大學(xué)博士學(xué)位，1998年到首都師范大學(xué)數(shù)學(xué)系工作,99年破格教授，02年擔(dān)任博士生導(dǎo)師。杜少飛教授是代數(shù)組合領(lǐng)域的知名專家，很多工作深受國內(nèi)外同行好評。到目前為止其主要學(xué)術(shù)貢獻(xiàn)有：給出了半對稱圖的群論刻畫，這樣為近期將置換群和群與圖方面的方法和結(jié)果用于半對稱圖的研究提供了有力的工具，進(jìn)而完成了點(diǎn)數(shù)為2pq 的半對稱圖的分類；找到并證明了最小點(diǎn)數(shù)的本原半傳遞圖；在給定基圖為完全圖，覆蓋變換群為初等交換群Z_p^n的情況下做了嘗試，分別完成了n=2,3的分類；給出了覆蓋變換群為初等交換群的圖的正則覆蓋中自同構(gòu)的提升的充要條件及線性算法；完成了二面體群2-弧傳遞Cayley圖的分類；對于簡單圖的正則嵌入，通過用其自同構(gòu)群來研究它，用陪集圖來定義所謂的代數(shù)地圖，從而為置換群理論在地圖的分類中的應(yīng)用提供了好的語言；給出了自同構(gòu)群為單群PSL(3, p)的不可定向地圖的分類等。到目前為止共主持了13項包括國家自然科學(xué)基金、教育部重點(diǎn)項目、國際合作項目等在內(nèi)的科研課題。
講座主題：Complete regular dessins and skew-morphisms of cyclic groups
專家姓名：胡侃
工作單位：浙江海洋大學(xué)
講座時間：2018年5月10日上午9:30-10:30
講座地點(diǎn)：煙臺大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院341
主辦單位：煙臺大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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.
主講人介紹：
在斯洛伐克獲得哲學(xué)博士，斯洛伐克科學(xué)院數(shù)學(xué)研究所博士后，現(xiàn)為浙江海洋大學(xué)副教授。研究方向有：群與圖、群與地圖、拓?fù)鋱D論、涂鴉理論。
