I study the modular representation theory of finite groups. Here are some topics I am presently interested in or plan to study in the future:
- Local-to-global group theoretic conjectures such as Broue’s abelian defect group conjecture
- Finiteness conjectures such as Puig’s conjecture
- Biset functors and applications
- Endotrivial modules and generalizations, such as endotrivial complexes
- Categorification and diagrammatics
- Intersections of combinatorics and modular representation theory
Publications and Preprints
- S. K. Miller (In preparation, 2024). Galois descent of splendid Rickard equivalences between blocks of $p$-nilpotent groups.
- S. K. Miller (Submitted March 2024). On endotrivial complexes and the generalized Dade group.
- S. K. Miller (Submitted February 2024). Relatively endotrivial complexes.
- J. Breland, S. K. Miller (Submitted December 2023). Brauer pairs for splendid Rickard complexes.
- S. K. Miller (2024). Endotrivial complexes.
- To appear in Journal of Algebra. arXiv:2309.12138
- A. T. Benjamin, S. K. Miller (2023). A proof of the optimal leapfrogging conjecture.
- To appear in Involve. arXiv:2110.08319
- A. T. Benjamin, S. K. Miller (2018). Challenging knight’s tours.
- Math Horizons, 25(3), 18-21. PDF
Theses
- S. K. Miller (2017): The Combinatorial Polynomial Hirsch Conjecture, Harvey Mudd College Senior Theses, 109.