Project code



School of Mathematics and Physics

Start dates

February and October

Application deadline

Applications accepted all year round

This 3-year self-funded PhD will be based in the School of Mathematics and Physics and will be supervised by Dr Thomas Kecker and Dr Andrew Burbanks.

On this project, we will study the properties of solutions of certain recently-discovered classes of differential equations in the complex plane, which have movable singularities of algebraic type.

This property is a generalisation of the so-called Painlevé property, within which all singularities have to be poles in the complex plane.

The project will develop a theory of multi-valued analytic functions defined as solutions of these equations, and rigorously investigate their properties – such as the distribution of their singularities in the complex plane; the asymptotic behaviour of solutions in the limit where the independent variable tends to infinity; and the possibility of truncated solutions.

Fees and funding

Visit the research subject area page for fees and funding information for this project.

Funding availability: Self-funded PhD students only. 

PhD full-time and part-time courses are eligible for the UK Government Doctoral Loan (UK and EU students only).

Bench fees

Some PhD projects may include additional fees – known as bench fees – for equipment and other consumables, and these will be added to your standard tuition fee. Speak to the supervisory team during your interview about any additional fees you may have to pay. Please note, bench fees are not eligible for discounts and are non-refundable.

Entry Requirements

  • You'll need a good first degree from an internationally recognised university (minimum upper second class or equivalent, depending on your chosen course) or a Master’s degree in Mathematics or related subject.
  • In exceptional cases, we may consider equivalent professional experience and/or Qualifications.
  • English language proficiency at a minimum of IELTS band 6.5 with no component score below 6.0.

You should have a strong background knowledge in complex analysis and an interest in pursuing a vigorous research programme on the theory of differential equations in the complex plane, as this is a relatively pure, but nevertheless applicable area of mathematics.

How to apply

When you are ready to apply, please follow the 'Apply now' link on the Mathematics PhD subject area page and select the link for the relevant intake. Make sure you submit a personal statement, proof of your degrees and grades, details of two referees, proof of your English language proficiency and an up-to-date CV. Our ‘How to Apply’ page offers further guidance on the PhD application process.