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.