Mathematical interests
- Non/commutative tensor-triangular geometry
- Block theory and local-global modular representation theory of finite groups
- Intersections between representation theory and tensor-triangular geometry
- Invertible objects and Picard groups
- Permutation modules and their role in representation theory
Publications and preprints
| Title | Co-Authors | Journal | arXiv |
|---|---|---|---|
| 10. Re-framing the classification of ideals in noncommutative tensor-triangular geometry | Timothy de Deyn | 2510.23767 | |
| 9. Permutation twisted cohomology, remixed | 2509.00954 | ||
| 8. The Euler characteristic of an endotrivial complex | Nadia Mazza | Submitted | 2508.07404 |
| 15/2. Permutation Modules and Endotrivial Complexes | Advisor: Robert Boltje | Ph.D. Thesis, UC Santa Cruz | |
| 7. On functoriality and the tensor product property in noncommutative tensor-triangular geometry | Submitted | 2505.01899 | |
| 6. On endosplit $p$-permutation resolutions and Broue’s conjecture for $p$-solvable groups | Submitted | 2408.04094 | |
| 5. Galois descent of splendid Rickard equivalences between blocks of $p$-nilpotent groups | Proc. Amer. Math. Soc. 153 (5), 1893-1902 (2025) | 2405.16061 | |
| 4. The classification of endotrivial complexes | Adv. Math. 478, 110414 (2025) | 2403.04088 | |
| 3. Relatively endotrivial complexes | J. Pure Appl. Algebra, 229 (2), 107867 (2025) | 2402.08042 | |
| 2. Brauer pairs for splendid Rickard equivalences | Jadyn V. Breland | Submitted | 2312.10258 |
| 1. Endotrivial complexes | J. Algebra, 650, 173-218 (2024) | 2309.12138 | |
| 0. A proof of the optimal leapfrogging conjecture | Arthur T. Benjamin | Involve, 18 (1), 105–122 (2025) | 2110.08319 |
| -1/2. The Combinatorial Polynomial Hirsch Conjecture | Advisor: Mohamed Omar | Harvey Mudd College Senior Theses, 109 | |
| -1. Challenging knight’s tours | Arthur T. Benjamin | Math Horizons, 25 (3), 18-21 (2018) |
(Listed in chronological order)
Ongoing Projects
Here are some things I’m thinking about at the moment. More details will appear when they exist, or more likely, will be added to the above table.
- Tensor-triangular geometry vs. Tensor-exact or tensor-abelian geometry (w/ Timothy de Deyn)
- Integral permutation modules (w/ Juan Omar Gomez)
- Things involving permutation module categories for oligomorphic groups (w/ Nate Harman)
- Noetherianity of the (remixed) twisted cohomology ring
- Classification of central thick subcategories of a block algebra $kGb$
- Is the frame of smashing tensor-ideals spatial? (This is perhaps hard)