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: Asymptotic enumeration of graphical representations
Speaker: 甘芸松 Yunsong Gan (Southern University of Science and Technology)
Time: 16:00-17:00 (GMT+8), Sunday September 28th
Location: Zoom: 262 780 8767 (passcode: gts2025)
Abstract:
Recent breakthroughs on symmetry of Cayley (di)graphs show that almost all finite Cayley (di)graphs have the smallest possible automorphism group.
Extending the scope of these results, we enumerate (di)graphs admitting a fixed semiregular group of automorphisms with \(m\) orbits.
Moreover, we consider the more intricate inquiry of prohibiting arcs within each orbit, where the special case \(m=2\) is known as the problem of finding Haar graphical representations (HGRs).
We prove that the proportion of HGRs among Haar graphs of a finite nonabelian group approaches \(1\) as the group order grows.
In this talk, we will also discuss some findings obtained by using graphical representations in the context of Mckay-Praeger Conjecture and Polycirculant Conjecture.
The seminar is currently based at the Southern University of Science and Technology (SUSTech, 南方科技大学).