I primarily study the modular representation theory of finite groups.
Current focuses
- Local-to-global conjectures such as Broue’s abelian defect group conjecture
- Invertible objects such as endotrivial modules and complexes
- Intersections of modular representation theory and tensor-triangulated geometry
- Biset functors and applications
- Galois descent of representations
Future interests
- Categorification and diagrammatic categories
- Intersections of combinatorics and modular representation theory
- Counting conjectures such as Alperin’s weight conjecture
Publications and Preprints
- Galois descent of endosplit $p$-permutation resolutions
In progress
- Galois descent of splendid Rickard equivalences between blocks of $p$-nilpotent groups
Submitted May 2024
- On endotrivial complexes and the generalized Dade group
Submitted March 2024
- Relatively endotrivial complexes
Submitted February 2024
- Brauer pairs for splendid Rickard complexes
(with Jadyn V. Breland)
Submitted December 2023 - Endotrivial complexes
- A proof of the optimal leapfrogging conjecture
- Challenging knight’s tours
(with Arthur T. Benjamin)
Math Horizons, 25(3), 18-21 (2018)
Theses
- The Combinatorial Polynomial Hirsch Conjecture
Harvey Mudd College Senior Theses, 109.