My academic research interests are in geometric combinatorics and combinatorial optimization. My thesis advisor was Victor Reiner at the University of Minnesota. In my thesis I classified when incoherent f-monotone paths exist for on zonotopes in corank 1 and 2. The classification in corank 2 is pictured above. There are several (Z,f) pairs for which every f-monotone path on Z is coherent, which are the green families above. Although my results all proven by hand, I rely on computers to generate examples for conjectures and motivation for proofs.
In a former academic life I worked with Ezra Miller on A-hypergeometric functions, a topic in commutative algebra and combinatorics. Although I am no longer actively researching these topics, I remain interested in them and would enjoy returning to them some day.