- Operators on holomorphic function spaces: Toeplitz operators, Hankel operators,
and composition operators on various spaces of holomorphic functions in various
complex domains, including Bergman and Hardy spaces of the unit ball and the
- Complex analysis: characterizations and duality problems for various spaces of
holomorphic functions, including Bergman spaces, Besov spaces, the Bloch space,
Lipschitz spaces, and BMOA; function theory of Bergman spaces in the unit disk
and Fock spaces on the complex plane.
- Operator theory and operator algebras: operators in Cowen-Douglas classes,
operator theory related to the Bergman shift, invariant and reducing subspaces,
and C*-algebras of operators.
- Undergraduate courses taught: calculus, linear algebra, ordinary differential
equations, partial differential equations, general topology, algebraic topology,
differential geometry, probability, and statistics.
- Graduate courses taught: real analysis, complex analysis, functional analysis,
operator theory, operator algebras.