Complex differential equations with algebraic singularities
PhDs and postgraduate research
Self-funded PhD students only
School of Mathematics and Physics
Applications accepted all year round
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
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).
2021/2022 fees (applicable for October 2021 and February 2022 start)
PhD and MPhil
Home/EU/CI full-time students: £4,500 p/a**
Home/EU/CI part-time students: £2,250 p/a**
International full-time students: £17,600 p/a*
International part-time students: £8,800 p/a*
PhD by Publication
External candidates: £4,407*
Members of staff: £1,720
All fees are subject to annual increase. If you are an EU student starting a programme in 2021/22 please visit this page.
*This is the 2020/21 UK Research and Innovation (UKRI) maximum studentship fee; this fee will increase to the 2021/22 UKRI maximum studentship fee when UKRI announces this rate in Spring 2021.
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.
- 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
Please contact Dr Thomas Kecker (firstname.lastname@example.org) to discuss your interest before you apply, quoting the project code.
When you are ready to apply, you can use our online application form. 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.
If you want to be considered for this self-funded PhD opportunity you must quote project code MPHY4430219 when applying.