My research interests lie at the intersection of abstract algebra (typically groups) and combinatorics (typically graphs and/or finite geometries), that is, I like considering finite combinatorial objects through the lens of groups and groups through the lens of combinatorics. If you have interest in independent study and/or a potential research project, email me!
Melissa Lee (Honours at The University of Western Australia, 2014), Relative Hemisystems on the Hermitian Surface, co-supervised with John Bamberg.
Publication from this work: A note on relative hemisystems of Hermitian generalised quadrangles, Designs, Codes and Cryptography 81 (1), 2016, 131–144.
Ryan Oppenheim (Monroe Scholars Program, 2016), On the covering number of S14, Involve, 12 (1), 2019, 89–96. Supplementary material related to this paper can be found here.
Torger Olson (EXTREEMS-QED, 2017), Transitive PSL(2,11)-invariant arcs in PG(4,q), Designs, Codes and Cryptography, 87 (8), 2019, 1871–1879.
Yoongbok Lee (2017–2018 William & Mary Honors Fellow), Implementation and Analysis of the Nonlinear Decomposition Attack on Polycyclic Groups.
Santana Afton (Honors, 2017–2018), On prime order automorphisms of generalized quadrangles, Algebraic Combinatorics 3 (1), 2020, 143–160.
Cooper Spinelli (EXTREEMS-QED, 2018), Relative difference sets in nonabelian groups.
Gabrielle Tauscheck (Honors, 2018–2019), Partial Difference Sets in Nonabelian Groups and Strongly Regular Cayley Graphs. Publication related to this work can be found here.
Abigail Van Essendelft (Monroe Scholars Program, 2019), Mathematics of Art.
Kerry Wang (Monroe Scholars Program, 2019), Ovoids in generalized quadrangles of order (4,12).
Aditya Mohan (Independent research, 2019–2020), Coloring vertex-transitive graphs.
Samantha Phillips (Honors, 2020–2021), A survey of methods to determine quantum symmetry of graphs.
Nathaniel Healy (Honors, 2021–2022), Enumerating Switching Isomorphism Classes of Signed Graphs.
Ryan Pesak (Honors, 2022–2023), Automorphisms of a Generalized Quadrangle of Order 6.
Seth Nelson (Honors, 2024–2025), Character Theoretic Techniques for Nonabelian Partial Difference Sets. Preprint related to this work can be found here.
James Elmore (Honors, 2025–2026), Methods of Computational Search for Strongly Regular Graphs.