# 群与图讨论班 Seminars on Groups and Graphs

- 有限单群（有限单群分类定理，子群结构，共轭类等）
- 置换群与传递图
- 线性代数群与李型群
- 有限群的表示
- 有限$$p$$-群
- 图的谱理论

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.

- Finite simple groups (CFSG, subgroup structures and conjugacy classes)
- Permutation groups and transitive graphs
- Linear algebraic groups and Lie type groups
- Representations of finite groups
- Finite $$p$$-groups
- Spectral theory of graphs
If you are a young group theorist or graph theorist, and want to give a talk, please drop an email to Zhaochen Ding at dzha470@aucklanduni.ac.nz. We would also love to hear any suggestions you have for speakers. Don't worry if you have no new results -- we also warmly welcome any survey, or even a method that you find helpful, on any related topic.

## Time

Our usual time is Saturday 16:00-17:00 (GMT+8).

## Forthcoming Seminars

April 3rd: 郑莎莎 Shasha Zheng (University of Melbourne)
Graphical regular representations of finite groups
Zoom 616 601 4311 (password: gts2023)
April 17th: 周慧 Hui Zhou (Beijing University of Chemical Technology)
Zoom 616 601 4311 (password: gts2023)
May 15th: Kamilla Rekvényi (Imperial College London)
The orbital diameter of primitive permutation groups
Zoom 616 601 4311 (password: gts2023)

### The Next Seminar

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’.

## Current Organizers

The seminar is currently based at the Southern University of Science and Technology (SUSTech, 南方科技大学).