Permutation groups: bases and Saxl graphs-黄弘毅 (University of Bristol)
报告题目: Permutation groups: bases and Saxl graphs
报告人: 黄弘毅 (University of Bristol)
Abstract：Let be a permutation group on a finite set Ω. A base for G is a subset of Ω with trivial pointwise stabiliser, and the base size of G, denoted b(G), is the minimal size of a base for G. This classical concept has been studied since the early years of permutation group theory in the nineteenth century, finding a wide range of applications. Recall that G is called primitive if it is transitive and its point stabiliser is a maximal subgroup. Primitive groups can be viewed as the basic building blocks of all finite permutation groups, and much work has been done in recent years in bounding or determining the base sizes of primitive groups. In this talk, I will review some recent development of this study. In particular, I will give the first family of primitive groups arising in the O’Nan-Scott theorem for which the exact base size has been computed in all cases. I will also report on recent work concerning the Saxl graph of a base-two permutation group, which was recently introduced by Burness and Giudici.
报告人简介：黄弘毅，英国University of Bristol在读博士，国家留学基金委公派留学生，美国数学会《数学评论》评论员，澳洲组合数学会成员。研究方向为置换群论及相关组合结构。在J. Pure Appl. Algebra，Algebr. Comb. 等期刊中发表学术成果。曾受剑桥大学、帝国理工学院、洛桑联邦理工、墨尔本大学等高校邀请进行学术成果展示。