Elliptic and parabolic PDE on Manifolds with geometric singularities such as cusps, cones and edges
Quantisation of gravity coupled to matter via Ashtekar-Barbero-Sen variables and noncommutative geometry
K-theory of operator algebras and index theory.
Algebras of pseudo-differential operators and boundary value problems.
Constructive approaches to spectral triples.
Spectral theory with magnetic fields.
Operators on metric graphs (quantum graphs).