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
- Categorification
Publications and Preprints
- 7. The Euler characteristic of an endotrivial complex
(with Nadia Mazza)
In progress - 6. On endosplit $p$-permutation resolutions and Broue’s conjecture for $p$-solvable groups
Submitted August 2024
- 5. Galois descent of splendid Rickard equivalences between blocks of $p$-nilpotent groups
Submitted May 2024
- 4. On endotrivial complexes and the generalized Dade group
Submitted March 2024
- 3. Relatively endotrivial complexes
Submitted February 2024
- 2. Brauer pairs for splendid Rickard complexes
(with Jadyn V. Breland)
Submitted December 2023 - 1. Endotrivial complexes
- 0. A proof of the optimal leapfrogging conjecture
- -1. Challenging knight’s tours
(with Arthur T. Benjamin)
Math Horizons, 25(3), 18-21 (2018)
(Listed in chronological order)
Theses
- The Combinatorial Polynomial Hirsch Conjecture
Harvey Mudd College Senior Theses, 109.