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Christopher's research involves the study of association schemes, along with a new kind of mathematical object called a hypergroup. Association schemes are combinatorial structures which originally arose in statistics, but have since yielded applications to a wide variety of other fields, including coding theory, knot theory, graph theory, and the theory of combinatorial designs. Underlying each association scheme is an algebraic structure called a hypergroup, which is like a group except that the product of two elements is a set of elements, rather than a single element. Chris is especially interested in understanding how classical results in group theory can (or sometimes cannot) be generalized to association schemes and hypergroups.

Lately, Chris has become interested in exploring ways that virtual and augmented reality could be used to aid in the teaching of geometric concepts. He remembers how students used to laugh when, in teaching his multivariable class, he would muse that one day he would be able to draw a figure in the air with a special kind of pen, and everyone would be able to see his drawing suspended in space. He has noticed that such comments no longer elicit laughter. Please talk to Chris if you are interested in helping to design VR experiences!