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.