- Riemannian geometry
- Representation theory of finite groups
- Lebesgue integration and Fourier analysis
- Commutative algebra — missing proof of Nullstellensatz.
- Riemann surfaces
- Lie algebras — abandoned indefinitely.
- Arithmetic dynamics — in progress.
- Functional analysis — in progress.
- Geometric group theory and Gromov’s theorem
- Burnside groups
- Jacobson’s commutativity theorem
- Projective modules
- Artin-Wedderburn theorem
- Algebraic limits