PhD in Mathematics

PhD Studentship in “Non-uniformly elliptic problems in Optimal Transport” (2025)

What you get

• Fully-paid tuition fees for three and a half years.
• A tax-free bursary for living costs for three and a half years (£19,237 per annum in 2024/25).
• Additional financial support is provided to cover short-term and long-term
  travel.
• If you are not a UK national, nor an EU national with UK settled/pre-settled
  status, you will need to apply for a student study visa before admission.

Type of award

Postgraduate Research

PhD project

Optimal transportation is a highly active area of mathematics. In the last years a number of new insights have allowed to develop the mathematical theory further. Moreover, optimal transport has become increasingly relevant in applications such as data science, physics and engineering. In 2014, a linearisation ansatz was suggested for the Monge-Ampere equation and using this ansatz as a heuristic a number of far-reaching conjectures concerning the problem of finding a matching of two point-clouds which is minimal with regards to some cost function were made. This problem is known as optimal matching and can be seen as a special case of optimal transportation. The proposed linearisation ansatz has since been rigorously implemented in a growing body of work concerning not only optimal matchings, but also regularity of optimal transport maps.

Through the linearisation ansatz, it has become possible to attack problems in transportation through (elliptic) PDE techniques. In the last twenty years, the regularity theory of non-uniformly elliptic problems has received considerable attention and significant progress has been made. Non-uniformly elliptic problems are used to model materials with phase transitions and appear, for example, naturally in homogenisation problems.

The aim of this project is to transfer the techniques developed for non-uniformly elliptic problems to the setting of optimal transport and to extend the results obtained there for uniformly elliptic cost functions to the setting of non-uniformly convex costs.

Eligibility

Applicants must hold, or expect to hold, at least a UK upper second class degree (or non-UK equivalent qualification) in Physics/Mathematics, or a closely-related area, or else a lower second class degree followed by a relevant Master's degree.

This award is open to UK and International students

Deadline

31 January 2025 23:45

How to apply

Apply through the University of Sussex on-line system. 

https://www.sussex.ac.uk/study/phd/apply/log-into-account

Select the PhD in Physics/Mathematics, with an entry date of September 2025.

In the Finance & Fees section, state that you wish to be considered for studentship no APDE/2025/01.

We advise early application as the position will be filled as soon as a suitable applicant can be found.

Due to the high volume of applications received, you may only hear from us if your application is successful.

Contact us

If you have practical questions about the progress of your on-line application or your eligibility, contact mps-pgrsupport@sussex.ac.uk

For academic questions about the project, contact Dr Lukas Koch at lukas.koch@sussex.ac.uk

Timetable

We advise early application as the position will be filled as soon as a suitable applicant can be found.