I am interested in:
- algebraic structures such as polynomial rings, vector fields, and categories;
- topological structures such as projective space, knots, and differentiable manifolds;
- logical structures such as ordinals, spectra, and types;
- connections between these areas of study, including homology, homotopy type theory, and topos theory;
- applications of these topics to the sciences, including computer science and physics;
- applications of these topics outside the sciences, including education and law.