Description of Research
My research is centered in partial differential equations and
geometry analysis in complex variables. My past research
includes the following areas: interpolation sequences
for Hardy and Bergman spaces, invariant metrics, spectral domains in
several complex variables, domains with non-compact automorphism groups,
and compactness in the 
-Neumann problem.
Lately, I am interested in spectral theory of partial differential
operators, especially the -Neumann and Kohn
Laplacians.
Complex analysis and partial differential equations provide
key tools to many areas of sciences and engineering.
For example, the Laplace transform is essential in the study
of mechanical vibrations and electric circuits.
Many practical problems are modeled in partial differential equations.
The Laplace equation has important applications to hydrodynamics,
electrostatics, and heat conduction. The problems in complex analysis
and partial differential equations are not only
intrinsically interesting, but also have implications in other areas such
as potential theory, mathematical physics, and quantum mechanics.