Combinatorics, Matroids, Graph Theory
Fall 2014: M 191 Fairness and Social Justice
Ph.D., University of North Carolina, Chapel Hill
I study matroids, which are abstractions of finite graphs, geometries or sets of vectors. While matroids are abstract structures, they are exactly what specifies if the greedy algorithm will work. Thus, matroids arise naturally in optimization. Matroids are a part of a branch of mathematics called Combinatorics. Techniques in combinatorics allow us to find a shortest route between two cities, to schedule airplanes (or buses or whatever) in an optimal manner and to schedule workers to jobs (classes to final exam slots or...) optimally.
My work in matroids has ranged from the study of oriented matroids, to structural properties in binary and bicircular matroids. Recently, I am working on a general class of problems involving symmetry and matroids. This project has allowed me to involve undergraduates in my research. While much of my work has been theoretical, I did work on an applied problem that was presented by a semiconductor company. This problem involved improving the process of reverse engineering of computer chips. We used combinatorial properties to give a solution.