Geometric classification of complex differential equations

About the project

About the Project Applications are invited for a self-funded, 3 year full-time or 6 year part-time PhD project. The PhD will be based in the School of Computing, Mathematics and Physics and will be supervised by Dr Thomas Kecker and Dr Andrew Burbanks . In this project you will develop novel mathematical and computational techniques to advance the theory of ordinary differential equations in the complex plane. Project Highlights: The work on this project will: use cutting edge geometric techniques to classify ordinary differential equations develop computational skills using computer algebra systems such as Mathematica or similar make your own research impact by developing a mathematical theory in novel directions Project description: This project builds on recent advancements in the area of complex differential equations, in particular the classification of Painlevé and quasi-Painlevé differential equation and their solutions in the complex plane. Painlevé equations, though discovered at the start of the 20th century from a purely function theoretic viewpoint, nowadays play a vital role in mathematical physics and neighbouring disciplines. Quasi-Painlevé equations are much younger, having emerged only in the last two decades, and currently form an active area of mathematical research. You will use novel geometric techniques, such as computing the Okamoto's spaces of initial conditions for various classes of differential equations and Hamiltonian systems, to obtain new such systems, classify them by their intersection diagrams and Newton polygons of the Hamiltonian, and find bi-rational relationships between already known systems. The aim is to obtain a comprehensive overview of quasi-Painlevé systems and develop the theory around them. 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 an appropriate 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. International students will require a study visa from UKVI to pursue the degree in the UK. If the research is in a sensitive or technological subject, the student may also need to secure an Academic Technology Approval Scheme (ATAS) certificate from the UK Foreign Office. How to Apply We’d encourage you to contact Dr Thomas Kecker ( thomas.kecker@port.ac.uk ) to discuss your interest before you apply, quoting the project code. 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. When applying please quote project code MAP10690529 .

Research areas