Research

As a research assistant on the ARC DECRA-funded project “The existence and abundance of small bases of permutation groups,” I am currently investigating a generalisation of a graph defined on groups of base size 2 — the Saxl graph — to groups of arbitrary base size.

My limited research prior to that involved studying the maximal subgroups of the Monster sporadic simple group using Martin Seysen's revolutionary Python package mmgroup. For a semester-long research project, supervised by Dr. Tomasz Popiel, I constructed the 2-local maximal subgroups and four small non-local subgroups for which the class fusions to the Monster were not known, allowing these fusions to be found and added to the GAP Character Table Library. The construction of the odd-local and remaining non-local maximal subgroups forms the topic of my Honours project, supervised by Dr. Melissa Lee and Prof. Heiko Dietrich.

My Erdős number is 3. The following path provides an upper bound; for a lower bound, observe neither my collaborators nor I had worked on a paper at the turn of the millenium (Erdős died in 1996):

A. Pisani – H. Dietrich – J. Conway – P. Erdős

Journal Publications and Preprints

1. Computing the character table of a 2-local maximal subgroup of the Monster.
   Preprint (2025).
   arXiv: 2503.15857 • Associated Python Code
2. Explicit construction of the maximal subgroups of the Monster
   (with H. Dietrich, M. Lee, and T. Popiel).
   Preprint (2024).
   arXiv: 2411.12230 • Associated Python Code
3. Conjugacy class fusion from four maximal subgroups of the Monster
   (with T. Popiel).
   Journal of Computational Algebra 11 (2024) 100021.
   arXiv: 2404.051194 • DOI: 10.1016/j.jaca.2024.100021 • Associated Python Code