I have been studying Plurisubharmonic functions in several variables. Of interest is how much one can subtract from them such that they stay Plurisubharmonic.

This project is related to the so called bumping theorem which is an important ingredient in the building of Integral Kernels that are used to solve the Cauchy Riemann equations.

Another topic of interest to me is to study so called Envelopes of Holomorpy. In complex euclidean space in dimension two or higher there are many domains with the property that all functions that are holomorphic on the domain do have a holomorphic extension to a strictly larger domain. We want to study questions of the type : Given a domain what can I say about the largest domain to which the holomorphic functions extend (the so called Envelope of Holomorphy)

I also like to work on problems related to dynamical systems in Several Complex Variables.

For example: What can one say about the topology of so called Fatou Components. These are connected components of the set on which the family of iterates (Composition of a map with itself n times) is a normal family.