These are, broadly speaking, operator theory and operator algebras. Most recent work has been on abstract model theory for families of operators, and families of representations of algebras, as formulated by Jim Agler. Applications have included the study of model theory for the families of hyponormal contractions and -contractions. This work has been done in collaboration with Scott McCullough and Hugo Woerdeman.
Other areas of research interest include operator theory on Krein spaces (a type of indefinite metric space). Parts of this work was in collaboration with James Rovnyak.