这是群论和图论方向的线上系列报告,我们希望能够促进国内外青年学者(博士生为主)在群论和图论研究上的交流。报告主题分布在(但不限于)以下研究方向:
This is a platform for young group theorists and graph theorists (mostly PhD students) to talk about their research and related topics online. The topic can be anything related to group theory and graph theory, including but not limited to the following.
一般地,系列报告定期于北京时间每周三下午16:00-17:00进行。
Our usual time is Wednesday 16:00-17:00 (GMT+8).
Title: Graph growth of permutation groups
Speaker: Đorđe Mitrović (University of Auckland)
Time: 16:00-17:00 (GMT+8), Wednesday May 08th
Location: Zoom: 616 601 4311 (passcode: gts2024)
Abstract:
Let \(\Gamma\) be a finite connected graph and
let \(G\) be a vertex-transitive group of automorphisms of \(\Gamma\). The pair \((\Gamma, G)\) is locally-\(L\) if the group induced by the action of the stabiliser
\(G_v\) on the neighbourhood of a vertex \(v\) is permutation isomorphic to \(L\).~Using this language, a classical theorem of Tutte states that for locally-\(A_3\) and locally-\(S_3\) pairs, \(|G|\) grows linearly with \(|V(\Gamma)|\).
More generally, given a transitive permutation group \(L\), we are interested in determining the growth of \(|G|\) as a function of \(|V(\Gamma)|\) for locally-\(L\) pairs \((\Gamma, G)\).
We present new results on this topic and highlight an exciting connection with the study of eigenspaces of graphs over finite fields.
The seminar is currently based at the Southern University of Science and Technology (SUSTech, 南方科技大学).