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The Pure Mathematics Group is highly respected and has world-renowned researchers in the areas of analysis and geometry, and combinatorics.

Analysis is the study of sets, functions and limiting processes; geometry is the study of shape, position and space.  Our researchers are particularly active in complex analysis, complex iteration theory, continued fraction theory, dynamical systems, geometric measure theory and toric topology.

Combinatorics is the mathematics of discrete (usually finite) combinations and arrangements. Our researchers have particular interests in graph theory, permutation patterns, combinatorial designs and the theory of symmetric maps on surfaces.

We welcome all enquiries from potential students who want to work in these areas.

Qualifications available:

PhD or MPhil


For detailed information on current fees visit Fees and funding.

Entry requirements:

Minimum 2:1 (or equivalent)

Potential research projects

Analysis and geometry

  • Complex dynamics: the structure of the escaping set and dimensions of Julia sets of transcendental entire functions
  • Complex analysis: the boundary behaviour of analytic and subharmonic functions
  • Continued fraction theory
  • Hyperbolic geometry in complex analysis
  • Fractal geometry: the structure of sets and measures in Euclidean spaces
  • Applied analysis: renormalization theory and nonlinear dynamical systems
  • Toric topology


  • Graph theory: well-quasi-ordering; degree-diameter problem and cages
  • Combinatorial designs, including their automorphisms and embeddings
  • Pattern avoiding permutations and their connection with graph theory
  • Theory of symmetric maps on surfaces

Potential supervisors

  • Dr Silvia Barbina
  • Dr Robert Brignall
  • Dr Katie Chicot
  • Dr Ben Mestel
  • Dr Toby O'Neil
  • Dr Kathleen Quinn
  • Professor Phil Rippon
  • Dr Ian Short
  • Professor Jozef Širáň
  • Professor Gwyneth Stallard
  • Dr Bridget Webb
  • Dr Gareth Williams

Further information

If you have an enquiry specific to this research area please contact:

Mathematics and Statistics Research Secretary
+44 (0)1908 655552

For general enquiries please contact the Research Degrees Team via the link under ‘Your questions’ on the right of the page.