My research is in the areas of several complex variables and holomorphic dynamical systems. For my PhD thesis I mostly worked on basins of attraction for automorphisms of complex manifolds. It is well known that the basin of a single automorphism is always biholomorphic to complex Euclidean space, but the question is much harder for a compact family of automorphisms. This problem is related to stable manifolds in complex hyperbolic dynamics. You can find a copy of my thesis here. The main results of my thesis have been split into the following three articles:
Non-autonomous basins of attraction and their boundaries, with Erlend Fornaess Wold, published in the Journal of Geometric Analysis (2005) pdf.
Non-Autonomous Dynamics in P^k, published in Ergodic Theory and Dynamical Systems (2005) pdf.