Research

My research interests include combinatorics, convex geometry, metric geometry, algorithms, computational complexity.

Students:   I would love to talk with you about research project ideas in plane colorings, discrete isoperimetric inequalities, and metric cotype. I'd also love to talk with you about your research interests!


Articles

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An Efficient Approximation of the Traveling Salesman Polytope Using Lifting Methods, unpublished, but available on the arxiv: http://arxiv.org/abs/math/0610385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