Graph cohomology

I began working on projects studying the combinatorics of moment polytopes in my thesis. The motivation for these projects comes from the work of Goresky, Kottwitz and MacPherson, who prove that the equivariant cohomology of X can be encoded in a labeled graph G. I have worked on several projects to study the combinatorics of this graph and its labeling.

How is a graph like a manifold?
(with Ethan Bolker and Victor Guillemin) submitted.
Preprint math.CO/0206103
We describe the combinatorics of GKM graphs. This paper is currently being reworked into a more substantial monograph. We have added Catalin Zara as an author.
Equivariant cohomology, homogeneous spaces, and graphs
PhD Thesis, MIT 2002
Available in PDF
In particular, I would like to extend many of the ideas in the first paper to hypergraphs, as discussed in this thesis.

I am currently trying to understand much of this theory as extended to hypergraphs. I have also been spending a fair bit of time working on the monograph. I am also advising an undergraduate thesis on a project related to the combinatorics of this graph cohomology.