Hongyi Huang

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

1. 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
2. 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
3. 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
4. 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
5. On finite permutation groups of rank three
   joint with C.H. Li and Y.Z. Zhu
   22 pages, submitted
   arXiv: 2311.04057
6. Fixers and derangements of finite permutation groups
   joint with C.H. Li and Y.L. Xie
   33 pages, submitted
   arXiv: 2404.18753

Thesis

1. On valency problems of Saxl graphs of almost simple primitive groups with soluble stabiliser
   Supervisor: Professor Cai Heng Li
   Undergraduate thesis, SUSTech (2020) [pdf]
2. Bases for permutation groups and related problems
   Supervisor: Professor Tim Burness
   PhD thesis, UoB, in preparation.