I primarily study the modular representation theory of finite groups.

**Current focuses**

- Local-to-global conjectures such as Broue’s abelian defect group conjecture
- Invertible objects such as endotrivial modules and complexes
- Intersections of modular representation theory and tensor-triangulated geometry
- Biset functors and applications
- Galois descent of representations
- Categorification

## Publications and Preprints

**7. The Euler characteristic of an endotrivial complex**(with Nadia Mazza)

In progress**6.****On endosplit $p$-permutation resolutions and Broue’s conjecture for $p$-solvable groups**Submitted August 2024

**5.****Galois descent of splendid Rickard equivalences between blocks of $p$-nilpotent groups**Submitted May 2024

**4.****On endotrivial complexes and the generalized Dade group**Submitted March 2024

**3.****Relatively endotrivial complexes**Submitted February 2024

**2.****Brauer pairs for splendid Rickard complexes**(with Jadyn V. Breland)

Submitted December 2023**1.****Endotrivial complexes****0.****A proof of the optimal leapfrogging conjecture****-1.****Challenging knight’s tours**(with Arthur T. Benjamin)

Math Horizons, 25(3), 18-21 (2018)

(Listed in chronological order)

## Theses

**The Combinatorial Polynomial Hirsch Conjecture**Harvey Mudd College Senior Theses, 109.