Christopher's research involves the study of association schemes. This study originally arose in statistics, but has since yielded applications to a wide variety of other fields, including coding theory, knot theory, graph theory, and combinatorial designs. Many researchers view association schemes as a generalization of groups; thus, the entire corpus of literature on group theory has the potential to provide interesting questions one may ask about association schemes. For example, anyone having taken Math 321 (Foundations of Abstract Algebra) knows that the smallest group which is non-commutative (i.e. non-abelian) has six elements. In a recent collaboration (to appear in Communications in Algebra), Benjamin Drabkin '14 and Chris have found a new family of non-commutative association schemes with six elements, one for each Mersenne prime. As another example, Chris recently completed a paper with his collaborator Paul-Hermann Zieschang to prove an analogue of the Schur-Zassenhaus Theorem for association schemes.
Chris is also interested in ways in which algebraic notions have applications in the sciences and the humanities – for example, in how music theory can be enriched by the study of group theory, or how one can use representation theory to gain useful insights in the study of chemistry and physics.