I am a second year PhD student under the supervision of Professor John Smillie. I am interested in dynamical systems, in particular, complex dynamics.
Previously I studied my MMath at the University of Liverpool and undertook two projects supervised by Professor Mary Rees. These projects concerned the dynamics of quadratic polynomials. With Professor Smillie I have begun studying complex dynamics in two dimensions. I have also been studying the Homotopy Shadowing work of Ishii and Smillie (ArXiv preprint, journal link). Additionally, I have been reading important material related to one dimensional dynamics and I have begun studying the iterated monodromy group work of Nekrashevych.
I am also currently involved in a complex dynamics reading group. The aim is to provide a comprehensive introduction to this beautiful subject and understand some major tools used in current research. Details and a schedule can be found here.
'Descriptions of Compact Sets in C' by Douady describes pinched disc models for compact sets in the complex plane and introduces Hubbard trees. Occasionally I need to look at this paper but, as far as I am aware, it is not available online, which is inconvenient. Here is a scanned version of the paper.
Email: Thomas.Richards "at" warwick.ac.uk
Office: Room B0.13 Zeeman Building