We do research in complex analysis, several complex variables and complex geometry.
Much of our research is focused on pluripotential theory and its applications to complex geometry as well as certain aspects of analytic function theory. Pluripotential theory is a nonlinear analog of the classical potential theory for subharmonic functions. The main objects of study are plurisubharmonic functions and the complex Monge-Ampere operator (ddcu)n – a generalization of Laplace's operator. In the theory of analytic functions we are mainly interested in ideals and spectrum for algebras of analytic functions, in particular Gleason's problem. In connection with this, we are also interested in domains of existence and envelopes of holomorphy for classes of analytic functions.