PhD Studentship in Mathematical Sciences

Postgraduate (PhD) Studentship in Mathematical Sciences at University College London

"Numerical methods for mean field games"

UCL Department / Division: Mathematics
Location of position: London
Duration of Studentship: 4 years
Stipend: Approximately £21,000 per annum

Vacancy Information

Applications are invited for an PhD Studentship in Mathematical Sciences. The studentship will be based in the Department of Mathematics at UCL and will supervised by Dr Iain Smears (UCL).

Mean field games originate from models of the Nash equilibria in games of stochastic optimal control with many players. In mathematical terms, they result in a system of nonlinear PDE consisting of a Hamilton-Jacobi-Bellman equation and a Fokker-Planck equation. Mean field games have become an exciting and highly active area of research, with a wide variety of applications and a rich mathematical theory. The numerical solution of these problems remains generally challenging because of the nonlinearity and the full space-time coupling of the system.

This PhD project aims to explore the design and analysis of numerical methods for mean field games. Possible directions of research include the analysis of numerical methods in the deterministic limit, the development of advanced space-time solvers for the efficient solution of the systems, or the analysis of a posteriori error bounds and adaptive methods. 

The project will involve analytical and numerical work. Interested applicants are encouraged to contact the primary supervisor Dr Iain Smears (i.smears@ucl.ac.uk) to discuss this project further. 

Studentship Description

The studentship includes tuition fees at the Home (UK) rate, a stipend of approximately £21,000 per annum, and an allowance to support research and training costs. Stipends will be set by the UKRI standard rate which will be confirmed later in 2024. Teaching-Assistant work may be involved. The studentship will be tenable for four years. 

Person Specification

Applicants should possess a good honours degree (1st Class) in Mathematics, or an equivalent qualification from other countries. Some background knowledge of numerical analysis and partial differential equations is desirable.

Application Process

Apply for the PhD programme in Mathematical Sciences at UCL, by completing the UCL Postgraduate Application on-line form available at: https://www.ucl.ac.uk/prospective-students/graduate/apply

Please also fill in the EDI form once you have submitted your application (this is for monitoring purposes only and will not affect your application): https://forms.office.com/e/GwLSBCQpvD

Questions about this project should be addressed to the primary supervisor Dr Iain Smears (i.smears@ucl.ac.uk) in the first instance.

General questions about PhD admissions can be addressed to the Graduate admissions tutor for Applied Mathematics, Dr Robb McDonald (n.r.mcdonald@ucl.ac.uk)

Closing Date:  3rd April 2024
Studentship Start Date: 1st October 2024