Research
My main interest of research is in group theory, mostly finite groups. I have a particular interest in permutation groups, as well as some related structures in combinatorics (e.g. transitive graphs). I'm also interested in finite simple groups, especially their subgroup structures and conjugacy classes.
More specifically, I mainly work on base sizes (the minimal size of a base) of finite permutation groups.
This has been studied since 19th century when permutation group theory was still young, finding a wide range of connections to other areas.
In my recent paper, I determine the precise base size of every finite primitive permutation group of diagonal type.
In terms of the O'Nan-Scott theorem (5-type version), this is the first family of primitive groups for which people have a complete answer on base sizes.
In 2022, I participated in the Simple groups, representations and applications programme at the Isaac Newton Institute in Cambridge. A brief description of my research on base-two primitive groups and their Saxl graphs up to that time can be found in my poster for this programme.
My Erdős number is 3. For example, there are two disjoint geodesics:
- H.Y. Huang -- T.C. Burness -- Á. Seress -- P. Erdős
- H.Y. Huang -- C.H. Li -- P.P. Pálfy (or J. Širáň) -- P. Erdős
Articles and preprints
- On valency problems of Saxl graphs
joint with J. Chen
Journal of Group Theory 25 (2022), 543-577.
arXiv: 2012.13747 | doi: 10.1515/jgth-2021-0123 | MathSciNet: MR4415978
- On the Saxl graphs of primitive groups with soluble stabilisers
joint with T.C. Burness
Algebraic Combinatorics 5 (2022), 1053-1087.
arXiv: 2105.11861 | doi: 10.5802/alco.238 | MathSciNet: MR4511160
- On base sizes for primitive groups of product type
joint with T.C. Burness
Journal of Pure and Applied Algebra 227 (2023), Paper No. 107228, 43 pp.
arXiv: 2202.02816 | doi: 10.1016/j.jpaa.2022.107228 | MathSciNet: MR4478370
- Base sizes of primitive groups of diagonal type
Forum of Mathematics, Sigma 12 (2024), Paper No. e2, 43 pp.
arXiv: 2303.14290 | doi: 10.1017/fms.2023.121 | MathSciNet: MR4685056
- On finite permutation groups of rank three
joint with C.H. Li and Y.Z. Zhu
22 pages, submitted
arXiv: 2311.04057
- Fixers and derangements of finite permutation groups
joint with C.H. Li and Y.L. Xie
33 pages, submitted
arXiv: 2404.18753
Thesis
- On valency problems of Saxl graphs of almost simple primitive groups with soluble stabiliser
Supervisor: Professor Cai Heng Li
Undergraduate thesis, SUSTech (2020) [pdf]
- Bases for permutation groups and related problems
Supervisor: Professor Tim Burness
PhD thesis, UoB, in preparation.