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Complex differential equations with algebraic singularities


Project Description

Applications are invited for a fully-funded three year PhD to commence in October 2019.

The PhD will be based in the School of Mathematics and Physics and will be supervised by Dr Thomas Kecker and Dr Andrew Burbanks.

Project description
In this project we will study the properties of solutions of certain only relatively recently discovered classes of differential equations in the complex plane which have the property that all their movable singularities are of algebraic type. This property is a generalisation of the so-called Painlevé property, where all singularities have to be poles in the complex plane, introduced by French mathematician Paul Painlevé and his school already in the 1900’s. 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.


Entry Requirements

General admissions criteria
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.

Specific candidate requirements
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
We’d encourage you to contact Dr Thomas Kecker ( ) 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 funded PhD opportunity you must quote project code MPHY4430219 when applying.

Funding Notes

Candidates applying for this project may be eligible to compete for one of a small number of bursaries available. The bursary is available to UK and EU students only and covers tuition fees and an annual maintenance grant in line with the RCUK rate (£14,777 for 2018/19). The Faculty of Technology may fund project costs/consumables up to £1,500 p.a.

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