Complex differential equations with algebraic singularities
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.
- 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 and select ‘Mathematics and Physics’ as the subject area. 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.