My research is mainly in two areas:
1. complex dynamics, in particular the escaping set of a transcendental meromorphic function, and its relationship to the Fatou and Julia sets of the function,
2. function theory, in particular the boundary behaviour of meromorphic functions and subharmonic functions.
Together with Professor Gwyneth Stallard, I lead the complex dynamics group at the OU, including a Research Associate, a Visiting Research Associate and two PhD students, and our activities often include other complex analysts in the Department.
Gwyneth Stallard and myself are currently working on a project to investigate a surprising link that we identified between two open conjectures in complex dynamics: Baker's conjecture and Eremenko's conjecture. The project has been funded by two EPSRC grants which together cover five years, at 0.5FTE each:
EP/H006591/1: Baker's conjecture and Eremenko's conjecture: a unified approach
EP/K031163/1: Baker's conjecture and Eremenko's conjecture: new directions
Our Research Associate, Dave Sixsmith, is funded by the following grant from the EPSRC:
EP/J022160/1: Dimensions in complex dynamics: spiders' webs and speed of escape
Open University teaching
My main teaching contributions have been to the following Open University courses: MST121 Using mathematics, MS221 Exploring mathematics, M208 Pure mathematics, M337 Complex analysis, M832 Approximation theory.