My research interests include representation theory of Lie groups and Lie algebras, combinatorics, and applied algebra, but I am interested in all areas of math, physics, and science in general.
I love teaching multivariable calculus and linear algebra, but also advanced courses on differential equations, differential geometry, and Lie groups and Lie algebras. I've supervised senior capstones on gauge theory and particle physics, quantum chemistry and representation theory of symmetry groups, dynamical systems in neurobiology, optimization in mathematical oncology, and more. Working at Lawrence gives me the opportunity to develop meaningful academic mentoring of our students, who quickly advance beyond the basics of calculus and linear algebra, and are highly motivated to dive into the beauty and discovery of advanced mathematics.
I've done research in the differential geometry of minimal submanifolds, Hilbert series for representations of Lie superalgebras, facet volumes of polytopes and the polytope inequality (which generalizes the triangle inequality), algebraic statistics of logarithmic Voronoi cells, shelling orders of matroid polytopes, tensegrity frameworks and their catastrophe discriminants, branching rules for representations of the general linear group to the symmetric group, and representations in spaces of harmonic polynomials. Most recently I showed how to determine generic rigidity of bar-joint frameworks in any dimension using the combinatorics of a directed line graph and Young tableaux.
