4 Year GTA - Beyond Critical Slowing Down: development of Early Warning Signals of tipping points based on Extreme Value statistics and tail dependence.

About the Project

Open to UK Applicants only

Mathematics are offering 3 fully-funded Graduate Teaching Assistant (GTA) PhD studentships available for UK applicants, starting in September 2026.

Graduate Teaching Assistantships allow research students to fund their PhD through part-time teaching work with the University.

A Graduate Teaching Assistant is responsible to the Head of School and is expected to undertake teaching or other duties within the School - not normally exceeding 8-10 contact hours per week - while undertaking research leading to a PhD.

Approximately 80% of their time will be spent on their doctoral research and 20% on their GTA responsibilities. Training is provided to help Graduate Teaching Assistants develop their teaching related skills and enhance their professional competencies.

Project highlights

Tipping points

Multivariate Extreme Value statistics

Climate and environmental modelling

Project description

The study of Tipping Points (TP) like the possible collapse of the Atlantic Meridional Overturning Circulation (AMOC) is a major research area for their potential impact on society. Mathematically TPs correspond to bifurcations in multi-stable systems with competing attractors, where crossing a critical value of a parameter due to an external forcing leads to abrupt changes in the state of the system. A key scientific goal is the development of Early Warning Signals (EWS) to anticipate the approach to a TP from the analysis of observational data. Traditional EWS are based on the concept of Critical Slowing Down (CSD), which predicts the increase of variance and temporal autocorrelation of physical observables near a TP. CSD is based on drastic assumptions on the properties of the dynamics, likely not to hold in real, high-dimensional systems. This has led to an increased interest in the development of new EWS. CSD-based EWS focus on typical fluctuations. Transitions are instead usually triggered by anomalous fluctuations that belong in the tails of the distribution of the observables. Effective EWS can thus be built based on the properties of rare fluctuations that explore the vicinity of a competing attractor without completing full transitions. Here we will use Extreme Value Theory (EVT) to develop EWS based on changes in tail statistics when approaching a TP. We will exploit recent results in EVT and spatial statistics on asymptotic dependence for multivariate distributions. These techniques will be applied to models of the AMOC of different complexity, from stochastic box models with different types of noise (from white to Lévy noise), to full numerical climate models, to real observational data. The project is positioned at the interface between statistics, stochastic processes, dynamical systems and climate science, and its output could lead to further applications in ecology, finance and other fields.

Project enquiries to Dr. Francesco Ragone fr120@leicester.ac.uk

Application enquiries to pgrapply@le.ac.uk

To apply please refer to the application advice and use the application link athttps://le.ac.uk/study/research-degrees/funded-opportunities/maths-gta

Start 21 September 2026

Funding Notes

The 4 year GTA funded studentships provide:

• A combined teaching and stipend payment, currently. for 2026/7 this will be £21,805 per year, paid in monthly instalments
• Tuition fees at UK rates