### In Submission

- Subtour Elimination Constraints Imply a Matrix-Tree Theorem SDP Constraint for the TSP, with David P. Williamson.
- Semidefinite Programming Relaxations of the Traveling Salesman Problem and Their Integrality Gaps, with David P. Williamson.
- Characterizing the Integrality Gap of the Subtour LP for the Circulant Traveling Salesman Problem, with David P. Williamson.
- Root Cones and the Resonance Arrangement, with Karola Mészáros and T. Kyle Petersen.
- Mathematics of Nested Districts: The Case of Alaska, with Sophia Caldera, Daryl DeFord, Moon Duchin, and Cara Nix. (Based on work with undergraduate students at the 2018 Voting Rights Data Institute.) See also the project GitHub.

### Working Papers

- Hardness of Matroid Inclusion, with Robert Kleinberg.

### Publications

- The Unbounded Integrality Gap of a Semidefinite Relaxation of the Traveling Salesman Problem, with David P. Williamson. SIAM Journal on Optimization 28:2073-2096, 2018.
- The Mean(est) Voting System, with David Lingenbrink and Michael Orrison. Math and Voting special issue of Math Horizons, 2016. (Based on undergraduate work at Harvey Mudd)
- Permutation Patterns in Latin Squares, with Michael Earnest. The Australasian Journal of Combinatorics, 2014. (Based on undergraduate work at the ETSU Math REU)
- Logarithmic Representability of Integers as k-Sums, with Anant Godbole, Vince Lyzinski, and Yan Zhuang. Erdos Centennial Conference volume of Integers, 2013. (Based on undergraduate work at the ETSU Math REU)

I have four internal papers within industry. Details are available on request.