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Bases for primitive permutation groups

黄弘毅 Hong Yi Huang

University of Bristol

Time: 16:00-18:00 (GMT+8), Tuesday May 24th, 2022
Location: Tencent Meeting

Abstract: Let \(G \leqslant \mathrm{Sym}(\Omega)\) be a permutation group and recall that a base for \(G\) is a subset of \(\Omega\) with trivial pointwise stabiliser. Bases have been studied for many decades and an ambitious project initiated by Jan Saxl in the 1990s seeks to determine the primitive groups with a base of size \(2\). In recent years, there has been significant progress towards this goal and I will review some of the latest developments. 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. Some of the new results are based on recent joint work with Tim Burness.

Host: 谢贻林 Yilin Xie