My Research

Doctorate in Mathematics:  University of North Carolina, Chapel Hill, NC.   fall 1995.  Advisor: James D. Stasheff.

Areas of Research :  Algebraic Combinatorics and Applied Graph Theory.

I am interested in both graph theory and abstract algebra, particularly in using algebraic techniques to achieve graph theoretic results. My recent work has been primarily with graph polynomials, constructing them and embedding them in algebraic structures sufficiently rich to extract new information from them. I have been able to use Hopf-algebras to derive new identities for the Martin polynomials of both oriented and unoriented Eulerian graphs, as well as for the Tutte polynomial along the diagonal y = x.  Recently, I have been working with generalized dualities of graphs in surfaces and topological graph polynomials.  My interests also include applications of graph theory to problems arising from computer chip design and from DNA sequencing and biomolecular computing.
 
A current area of major interest is using graph theoretical technics to find optimal design strategies for nanoscale DNA self-assembly processes.  This work can be found here:  Self-Assembly Design Strategies Website 
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