Research

My research falls in the general area of algebraic combinatorics. I am mainly interested in graphs that have a large amount of symmetry. By a “large amount” of symmetry, I mean that for any two vertices of the graph, there is a symmetry of the graph which maps one vertex to the other. There are natural questions about such graphs that I consider such as: If a graph has many symmetries, what are all of the symmetries of the graph? How can one tell if two graphs that have some common symmetries are isomorphic? What is the most efficient way of describing such a graph in terms of some symmetries as well as a single vertex and its neighbors? I am also interested in the group theoretic tools needed to tackle such problems, namely permutation group theory, and I also consider similar problems for other types of combinatorial objects such as codes and hypergraphs. .