In teaching, I have found Federico Ardila's axioms helpful as a reminder of the basic principles from which to grow. These are, (1) Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries, (2) Everyone can have joyful, meaningful, and empowering mathematical experiences, (3) Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs, and (4) Every student deserves to be treated with dignity and respect.
In research, I try to connect geometry with optimization, algebra, and combinatorics, and I am interested in all areas of math, physics, and science in general. 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.
