Research

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.

Pertubed Basins of Attraction, published in Mathematische Annalen (2006)
pdf.

More recent work can be downloaded below:

Attracting Basins of Volume Preserving Automorphisms of C^k, with Liz Vivas and Erlend Fornaess Wold, preprint
pdf.

Degree Estimates for Polynomials Constant on a hyperplane, with John P. D'Angelo and Jiri Lebl, to appear in Michigan Math J.
pdf.

Polynomials Maps that are roots of power series, to appear in Math. Z.
pdf.

More to come soon..