My current focus is the modular representation theory of finite groups. In particular:
- Local-to-global conjectures such as Broue’s abelian defect group conjecture
- Finiteness conjectures such as Puig’s conjecture
- Biset functors and applications
- Endotrivial modules and generalizations
I am also interested in combinatorial methods within modular representation theory.
- S. K. Miller, A. T. Benjamin (2023), A proof of the optimal leapfrogging conjecture, Involve (to appear) arXiv
- A. T. Benjamin, S. K. Miller (2018): Challenging knight’s tours, Math Horizons 25:3, 18-21. PDF
Preprints and projects
- S. K. Miller, Relative endotrivial complexes and restriction (in progress)
- J Breland, S. K. Miller, Brauer pairs for splendid Rickard complexes (in progress)
- S. K. Miller, Endotrivial complexes. (submitted for publication) (2023) arXiv
- S. K. Miller (2017): The Combinatorial Polynomial Hirsch Conjecture, Harvey Mudd College Senior Theses, 109.