My primary mathematical interests are in the field of groups, graphs, and geometries. I'm involved in the program of the classification of finite primitive distance-transitive graphs, and in the program of classifying vertex stabilizer amalgams of locally s-arc transitive graphs with s ≥ 4.
My research has been mainly concentrated on
Distance-regular and Distance-transitive graphs
Sporadic finite simple groups and their geometries
Generalized polygons and their extensions
Permutation Groups
Locally s-transitive graphs
Multiplicity-free permutation representations