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.
  • A. T. Benjamin, S. K. Miller (2023). A proof of the optimal leapfrogging conjecture.
  • A. T. Benjamin, S. K. Miller (2018). Challenging knight’s tours.
    • Math Horizons, 25(3), 18-21. PDF


  • S. K. Miller (2017): The Combinatorial Polynomial Hirsch Conjecture, Harvey Mudd College Senior Theses, 109.