Mathematics: Fully Funded EPSRC PHD Scholarship: Analysis and Numerics of Stochastic Partial Differential Equations

 Funding providers: EPSRC

Subject areas: Mathematics

Project start date: 

• 1 April 2023 (Enrolment open from mid–March) 
• 1 July 2023 (Enrolment open from mid-June) 

Supervisors:

• Professor Jiang-Lun Wu (j.l.wu@swansea.ac.uk)
• Dr Dmitri Finkelshtein

Aligned programme of study: PhD in Mathematics

Mode of study: Full-time 

Project description: 

Since the early seminal work of mathematical physicist Giorgio Parisi (Nobel Prize laureate in Physics in 2021) and the revolutionary work of the 2014 Fields Medalist Sir Martin Hairer, Stochastic Partial Differential Equations (SPDEs) becomes a very active research field with many cutting-edge and challenge research topics, and with diverse applications to real world problems. This project will investigate qualitative and quantitative properties of stochastic partial differential equations driven by Brownian motion and/or fractional Brownian motion, alpha-stable processes, point processes (Poisson and beyond), focusing on stochastic heat equations, stochastic conservation laws, and stochastic Burgers/KPZ equations. The approach consists of probabilistic, analytic and computational methods. The project is suitable to a student who has a solid foundation in probability theory, functional analysis and/or numerical analysis, with a moderate knowledge of partial differential equations. The student working on this project would first be trained in techniques spanning a diverse range of disciplines: stochastic processes and random fields, stochastic calculus, computational and statistical methods with simulations, and selected topics on partial differential equations. They would then develop the well posedness of the concerned stochastic equations and corresponding numerical schemes (if interested). They would also try to develop new equations, linking to advanced modelling in applied subject areas or industrial mathematics. 

Eligibility

Candidates must normally hold an undergraduate degree at 2.1 level or master’s degree with a minimum overall grade at ‘Merit’ (or Non-UK equivalent as defined by Swansea University).

English Language requirements: IELTS 6.0 Overall (with no individual component below 5.5) or Swansea recognised equivalent.

Due to funding restrictions, this scholarship is open to applicants eligible to pay tuition fees at the UK rate only, as defined by UKCISA regulations.