Personal Statement
I am a member of the Dynamical Systems group led by Prof. Lasse Rempe. My research belongs to the area known as Complex Dynamics, which lies at the interplay between Dynamical Systems and Complex Analysis. More precisely, I study the iteration of transcendental entire functions and holomorphic self-maps of the punctured plane. I am interested in questions such as the existence of wandering domains or understanding the structure of the escaping set.

Research Overview
I work in Complex Dynamics. More precisely, I study the iteration of transcendental entire (or meromorphic) functions. In my PhD thesis, under the supervision of Prof Phil Rippon and Prof Gwyneth Stallard at The Open University, I studied the escaping set of transcendental self-maps of the punctured plane. An example of such maps is the complex Arnold standard family.

Currently, I am working on the topology and dynamics of wandering domains (and their boundaries). In a recent work with Lasse Rempe and James Waterman, we proved that wandering domains of entire functions may form Lakes of Wada and that escaping wandering domains may have non-escaping points on their boundaries (known as maverick points). We also constructed a counterexample to Eremenko’s conjecture concerning the bounded components of the escaping set of transcendental entire functions.

I am also interested in other subjects such as the Hausdorff dimension and computational complexity of Julia sets and several subsets thereof, which are two different ways of measuring how complicated Julia sets can be.