Overview
Our dynamical systems research group has interests in holomorphic dynamics and in 1- and 2-dimensional topological dynamics. Ongoing research is focussed on transcendental dynamics, mating of polynomials, quasiconformal geometry, Thurston maps, and pseudo-Anosov maps. You will work, supervised by members of the group, on one or more of these active research areas.
About this opportunity
This project will give you the opportunity to get involved in one of the two most active research areas in modern dynamical systems theory: holomorphic dynamics, and low-dimensional topological dynamics. Members of the research group have expertise as well as ongoing research in the following areas:
- Transcendental dynamics, which studies the iteration of transcendental entire and meromorphic functions on the complex plane. Topics in this area include the topology and dynamics of wandering domains, the dimension and computational complexity of Julia sets, and the iteration of holomorphic self-maps of the punctured plane.
- Mating of polynomials – a way to combine the dynamics of two polynomials to form a new dynamical system. This operation also appears in the settings of Kleinian groups and random geometry, these deep connections provide motivation and cross-fertilization.
- Quasiconformal geometry – the study of properties of metric spaces which are invariant under scalings. The quasiconformal and quasisymmetric maps which appear in this context generalize conformal maps, and appear naturally in complex analysis and in geometric group theory.
- The dynamics of surface homeomorphisms, a research area based in William Thurston’s foundational classification theorem for surface homeomorphisms.
The choice of topic and supervisor will be made following discussions with you, and will be based on your particular mathematical background and interests. We expect that you will spend most of the first year of the programme on training. This will involve both studying the theory needed to bring you to the point where you can start to do research in your area, and developing your skills in mathematical writing and presentation. The remaining time will be spent primarily on original research under the guidance of your supervisor.
You will have opportunities to discuss mathematics and to collaborate with other Ph.D. students, with postdoctoral researchers, and with the academic staff in the Departments; to participate in our seminar program; and to travel to seminars and conferences in the UK and abroad.