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.