Research

My research interests include the intersection of combinatorics, convex geometry, metric geometry, and computation. Recently, my research has focused on using computational and mathematical techniques to address gerrymandering and understand the space of redistricting maps.

Students: I would love to talk with you about research project ideas to adapt the GEO metric to address racial gerrymandering, and other ideas I have in the study of redistricting maps. I'm also interested in using machine learning techniques to improve medical care, particularly for marginalized communities. I'd also love to talk with you about your research interests!

Articles

The Geography and Election Outcome (GEO) Metric: An Introduction with M. Campisi, T. Ratliff, and S. Somersille Election Law Journal: Rules, Politics, and Policy (2022)

Declination as a Metric to Detect Partisan Gerrymandering with M. Campisi, A. Padilla, and T. Ratliff Election Law Journal: Rules, Politics, and Policy (2019)

The Efficiency Gap, Voter Turnout, and The Efficiency Principle Election Law Journal: Rules, Politics, and Policy (2018)

Brunn-Minkowski Theory and Cauchy's Surface Area Formula with E. Tsukerman. The American Mathematical Monthly, Vol. 124, No. 10 ( 2017), pp. 922-929

A General Method to Determine Limiting Optimal Shapes for Edge-Isoperimetric Inequalities with E. Tsukerman. The Electronic Journal of Combinatorics 24(1) (2017), #P1.26

On Coloring Box Graphs with E. Hogan, J.O'Rourke, and C.Traub. Discrete Mathematics, Vol 338, Issue 2 (2015), p 209-216

Vertex Isoperimetric Inequalities for a Family of Graphs on Z^k with A.J. Radcliffe. The Electronic Journal of Combinatorics 19(2) (2012), #P45

Spaces of Small Metric Cotype, with K. Wildrick. Journal of Topology and Analysis Vol.2 Issue 4 (2010), p. 581-597

A Positive Semidefinite Approximation of the Traveling Salesman Polytope Discrete and Computational Geometry 38 (2007), p. 15-28

The Computational Complexity of Convex Bodies, with Alexander Barvinok, Surveys on Discrete and Computational Geometry, Contemporary Mathematics 453 (2008) p. 117-137

An Efficient Approximation of the Traveling Salesman Polytope Using Lifting Methods, unpublished, but available on the arxiv: http://arxiv.org/abs/math/0610385

My doctoral dissertation, entitled "The Computational Complexity of Convex Bodies."