Mathematical interests
- Non/commutative tensor-triangular geometry
- Modular representation theory of finite groups
- Intersections between representation theory and tensor-triangular geometry
- Invertible objects/Picard groups
- Permutation modules
Here is an informal summary (for experts in the field) of things I’m currently thinking about as of February 2026.
Publications and preprints
Listed in chronological order.
| 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 | Accepted, Represent. Theory | 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 | Submitted | 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 |
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) |