PhD in Topological or Holomorphic Dynamical Systems University of Liverpool in United Kingdom

The University of Liverpool's Department of Mathematical Sciences invites applications for a PhD position in Topological or Holomorphic Dynamical Systems. This opportunity is part of a vibrant research group with expertise in holomorphic dynamics and low-dimensional topological dynamics. The group’s ongoing research includes transcendental dynamics, mating of polynomials, quasiconformal geometry, Thurston maps, and pseudo-Anosov maps.

As a PhD student, you will work under the supervision of Dr T Hall, Dr D Meyer, or Dr D Marti-Pete, with the specific topic and supervisor determined based on your mathematical background and interests. The first year of the programme focuses on training, including theoretical study and the development of mathematical writing and presentation skills. Subsequent years are dedicated to original research, with opportunities for collaboration with other PhD students, postdoctoral researchers, and academic staff. You will also participate in seminars and may attend conferences in the UK and abroad.

Research areas within the group include:

• Transcendental dynamics: Iteration of transcendental entire and meromorphic functions, topology and dynamics of wandering domains, Julia sets, and holomorphic self-maps of the punctured plane.
• Mating of polynomials: Combining the dynamics of two polynomials to form new dynamical systems, with connections to Kleinian groups and random geometry.
• Quasiconformal geometry: Study of metric spaces invariant under scaling, with applications in complex analysis and geometric group theory.
• Dynamics of surface homeomorphisms: Based on Thurston’s classification theorem for surface homeomorphisms.

The studentship is funded by XTX Markets and covers full Home tuition fees (£5238 p.a. for 2026-27) and a maintenance grant (£21,805 p.a. for 2026-27) for 3.5 years. Additional funding is available for consumables and conference attendance. The studentship is open to both home and international applicants, but international fees are not covered. The University of Liverpool is committed to diversity and inclusion, and reasonable project adaptations are available for students with disabilities or other personal circumstances.

Applicants should have a strong mathematical background, typically with a first-class or upper second-class honours degree (or equivalent) in mathematics or a closely related subject. Interest or experience in dynamical systems or related areas is desirable. English language proficiency is required as per university standards. Candidates from all backgrounds are encouraged to apply, and additional support is available for students with disabilities.

To apply, complete the University of Liverpool online postgraduate research application form for a PhD in Mathematical Sciences, including the project title and reference number MPPR17. The application deadline is 3 April 2026.