Research Interests: Algebraic combinatorics, graph theory, and topology.

Personal website: www.personal.rhul.ac.uk/uxah/001.

My research centers on the interface of combinatorics and topology. I am particularly interested in the ways in which combinatorial and topological structures can be encoded in one another, and in exploiting such connections to solve hard problems in combinatorics and topology. I work extensively with topological extensions of graph polynomials and constructions. I am especially interested in using the additional topological structure to gain new understandings of classical polynomials (such as the chromatic, Tutte and Penrose polynomials), their evaluations, their connections between each other, and their connections with quantum invariants of knots and statistical mechanics.

I am also interested in in quantum and finite-type invariants of knots and applications of geometric group theory to knot theory. In addition, I have recently been working on applications of graph theory to biology.