Mathematical interests
- Non/commutative tensor-triangular geometry and the tensor product property, central generation
- Intersections between representation theory and tensor-triangular geometry
- Invertible objects and Picard groups
- Permutation modules, and their role in representation categories
- Pre-Tannakian categories
- Galois descent in modular representation theory
- Broue’s abelian defect group conjecture and local-global representation theory of finite groups
- Biset functors and applications
Current Projects
Here are some things I’m thinking about at the moment. More details will appear when they exist!
- Tensor-triangular geometry vs. Tensor-exact geometry
- A pointless aproach to nc-ttg
- Integral endotrivial complexes
- Things involving permutation module categories for oligomorphic groups
w/ Nate Harman
- Things relating to the noncommutative “tale of three spectra” and central generation
- Noetherianity of the (remixed) twisted cohomology ring
Publications and preprints
- 9. Permutation twisted cohomology, remixed
If you can prove noetherianity of the twisted cohomology ring, let’s talk!
- 8. The Euler characteristic of an endotrivial complex
w/ Nadia Mazza
Submitted - 7. On functoriality and the tensor product property in noncommutative tensor-triangular geometry
Submitted
- 6. On endosplit $p$-permutation resolutions and Broue’s conjecture for $p$-solvable groups
Submitted
- 5. Galois descent of splendid Rickard equivalences between blocks of $p$-nilpotent groups
- 4. The classification of endotrivial complexes
- 3. Relatively endotrivial complexes
- 2. Brauer pairs for splendid Rickard complexes
w/ Jadyn V. Breland
Submitted - 1. Endotrivial complexes
Undergraduate research
(Listed in chronological order)
Theses
- Permutation Modules and Endotrivial Complexes
Ph.D. Thesis, UC Santa Cruz
- The Combinatorial Polynomial Hirsch Conjecture
Harvey Mudd College Senior Theses, 109.