### In Submission

- Semidefinite Programming Relaxations of the Traveling Salesman Problem and Their Integrality Gaps, with David P. Williamson.
- Root Cones and the Resonance Arrangement, with Karola Mészáros and T. Kyle Petersen.

### Working Papers

- Hardness of Matroid Inclusion, with Robert Kleinberg.
- A Facet-Defining Inequality for the Circulant TSP, with David Williamson

### Publications

- Subtour Elimination Constraints Imply a Matrix-Tree Theorem SDP Constraint for the TSP, with David P. Williamson. Operations Research Letters 48(3):245-248, 2020.
- 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.) To appear in Statistics and Public Policy, 2020. See also the project GitHub.
- Characterizing the Integrality Gap of the Subtour LP for the Circulant Traveling Salesman Problem, with David P. Williamson. SIAM Journal on Discrete Mathematics 33(4):2452–2478, 2019.
- 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 several internal papers within industry. Details are available on request.