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.
Our usual time is Saturday 16:00-17:00 (GMT+8).
Title: Graphical regular representations of finite groups
Speaker: 郑莎莎 Shasha Zheng (University of Melbourne)
Time: 16:00-18:00 (GMT+8), Monday April 3rd
Location: Zoom: 616 601 4311 (password: gts2023)
Abstract: In this talk we are concerned with the automorphisms of Cayley graphs. Here are some natural questions: What kind of automorphism groups of Cayley graphs are ‘typical’; what kind of Cayley graphs are ‘common’? Viewing that ‘symmetry is rare’, a rough guess for the first question would be the groups that are ‘as small as possible’ in some sense, and one may guess for the second question that the Cayley graphs having the ‘smallest’ full automorphism groups would be the most common ones. We will estimate the number of GRRs of a given group with large enough order and show that almost all finite Cayley graphs have full automorphism groups ‘as small as possible’.
丁兆宸 Zhaochen Ding (University of Auckland)
黄弘毅 Hong Yi Huang (University of Bristol)
谢贻林 Yilin Xie (SUSTech)