I’m currently interested in various numerical invaraints of permutation groups. In particualr maximal irredundant base size and relational complexity.
During my PhD I have investigated maximal cocliques in the generating graphs of the symmetric and alternating groups. I am currently working on various group statistics for almost simple groups.
For my dissertation, I looked at Buildings, Chamber Graphs and Mathieu groups. Although the sporadic groups do not give rise to buildings, Ronan and Stroth constructed geometries for each of the sporadic groups that mimic the construction of buildings. I calculated the chamber graphs of these geometries for M_12, M_22, M_23 and M_24 in Magma, and investigated what “Building-like” behaviours their chamber graphs exhibited. I was also able to use more combinatorial approaches to calculate the chamber graphs of M_12 and M_22 by hand. The work on M_12 and M_22 had not appeared in the literature prior to this.
In the summer of my third year of undergraduate, I received a bursary from the London Mathematical Society to spend the summer researching. During this project, Peter Rowley and I wrote two papers. In one we calculated the chamber graphs of some GABs (Geometries that are Almost Buildings) and in the second we characterised the M_24-obits of octad triples