Research
Research
My research focuses on the representation theory of finite groups. Representation theory allows us to take an abstract group (which can be though of as arising from the symmetries of some object) and study it using the tools acssociated with matrix groups, which are much more concrete. For a more detailed introduction to the area for non-experts, I recommend this article that my colleagues have written.
My particular forcus in this area is on the character theory of so-called finite groups of Lie type (also called finite reductive groups). The classification of finite simple groups tells us that these groups are most (up to some definition of most) of the finite simple groups. The work in my Ph.D has revolved around the study of the action of Galois automorphisms on the character tables of these groups. See my publications below.
Preprints (Under Review)
3. The fields generated by character values of linear and unitary groups. Preprint
2. (with J. M. Martínez, N. Rizo, and A.A. Schaeffer Fry) Galois action on the principal block and generation of Sylow 3-subgroups Preprint.
Accepted/Published
1. Characters and the generation of Sylow 3-subgroups for almost simple groups, J. Algebra 701 (2026), 154--178. Published Version Preprint.
As is tradition I've included links to all of my collaborators websites: