Mathematical interests
- Modular representation theory of finite groups
- Intersections between representation theory and tensor-triangular geometry
- Non/commutative tensor-triangular geometry
- Invertible objects/Picard groups
- Permutation modules
- Tensor categories, pre-Tannakian categories, oligomorphic groups
Here is an informal summary (for experts in the field) of things I’m currently thinking about as of February 2026. Certain questions posed here may have or have not been answered.
In preparation / Ongoing projects
- Permutation twisted cohomology for all finite groups + Noetherianity(!!) (w/ J. O. Gómez)
- Tensor-triangular geometry of some oligomorphic groups (w/ N. Harman)
- Local Picard groups for permutation modules
- Questions about the stable permutation category (w/ M. Gallauer)
- Noncommutative tensor-triangular geometry of group algebras (w/ K. Vashaw)
- Something with central triangulated subcategories in the sense of Krause (maybe w/ G. Stevenson)
Publications and preprints
Listed in chronological order. 1 and 2 are undergraduate research.
| Title | Co-Authors | Journal | arXiv |
|---|---|---|---|
| 1. Challenging knight’s tours | Arthur T. Benjamin | Math Horizons, 25 (3), 18-21 (2018) | |
| 2. A proof of the optimal leapfrogging conjecture | Arthur T. Benjamin | Involve, 18 (1), 105–122 (2025) | 2110.08319 |
| 3. Endotrivial complexes | J. Algebra, 650, 173-218 (2024) | 2309.12138 | |
| 4. Brauer pairs for splendid Rickard equivalences | Jadyn V. Breland | J. Algebra, 691, 694-729 (2026) | 2312.10258 |
| 5. Relatively endotrivial complexes | J. Pure Appl. Algebra, 229 (2), 107867 (2025) | 2402.08042 | |
| 6. The classification of endotrivial complexes | Adv. Math. 478, 110414 (2025) | 2403.04088 | |
| 7. Galois descent of splendid Rickard equivalences between blocks of $p$-nilpotent groups | Proc. Amer. Math. Soc. 153 (5), 1893-1902 (2025) | 2405.16061 | |
| 8. On endosplit $p$-permutation resolutions and Broue’s conjecture for $p$-solvable groups | Represent. Theory 30, 151-174 (2026) | 2408.04094 | |
| 9. On functoriality and the tensor product property in noncommutative tensor-triangular geometry | Submitted | 2505.01899 | |
| 10. The Euler characteristic of an endotrivial complex | Nadia Mazza | Accepted, JPAA (Special edition for Dan Nakano’s 60th bithday) | 2508.07404 |
| 11. Permutation twisted cohomology, remixed | Submitted | 2509.00954 | |
| 12. Re-framing the classification of ideals in noncommutative tensor-triangular geometry | Timothy De Deyn | Submitted | 2510.23767 |
| 13. A semisimple subcategory of Khovanov’s Heisenberg category | Submitted | 2512.13968 | |
| 14. The classification of integral endotrivial complexes | Juan Omar Gómez | Submitted | 2605.31128 |
Proceedings
| Title | Proceedings |
|---|---|
| 1. Endotrivial complexes and remixed twisted cohomology | Oberwolfach Reports 23 (1), xxx-yyy (2026) |
Theses
| Title | Advisor | Link |
|---|---|---|
| 1. The Combinatorial Polynomial Hirsch Conjecture | Mohamed Omar | Harvey Mudd College Senior Theses, 109 (2017) |
| 2. Permutation Modules and Endotrivial Complexes | Robert Boltje | Ph.D. Thesis, UC Santa Cruz (2025) |