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mathematics PhD Projects, Programmes & Scholarships

We have 1,058 mathematics PhD Projects, Programmes & Scholarships

Uncovering the thinking skills that facilitate fraction learning (Ref: LN/RAM-SF1/2027)

Loughborough University

Mathematics Education Centre

Rational number learning is challenging for most students. Thus, there is an emerging interest in the skills that could act as conceptual scaffolds to support it. Read more

Supervisors: Dr R Abreu-Mendoza, Dr I Xenidou-Dervou

30 June 2027 PhD Research Project Self-Funded PhD Students Only

Spatial Association Modelling for Predicting and Forecasting Hazard Risks

The University of Manchester

Department of Mathematics

Climate led hazards do not occur randomly in space. They cluster, propagate, and interact across landscapes, communities, and infrastructure networks. Read more

Supervisor: Dr M Bhattacharjee

Year round applications PhD Research Project Funded PhD Project (Students Worldwide)

Model Theory of Complex Powers (KIRBYJ_U27SCI)

University of East Anglia

School of Mathematics

Primary Supervisor - Dr Jonathan Kirby. The field of complex numbers is in many ways the most elegant and important example of a mathematical structure in model theory. Read more

Supervisor: Dr J Kirby

24 February 2027 PhD Research Project Competition Funded PhD Project (UK Students Only)

Nonlinear waves in axisymmetric geometries (BLYTHM_U27SCI)

University of East Anglia

School of Mathematics

Primary supervisor - Prof Mark Blyth. The classical water wave problem provides a foundational framework for modelling gravity waves on liquid surfaces—from ocean swells to river flows. Read more

Supervisor: Dr M Blyth

24 February 2027 PhD Research Project Competition Funded PhD Project (UK Students Only)

[FSE PhD President's Doctoral Scholarship] Interdisciplinary Methods for Liquid Crystal-Based Biosensing

The University of Manchester

Department of Mathematics

Liquid crystals (LCs) are exceptionally versatile and functional mesophases that combine fluidity with the ordering of solids. LCs have tremendous potential as low-cost and non-invasive bio-sensors and have been used to sense glucose, proteins, enzymes, cells, micromolecules etc. Read more

Supervisors: Prof AM Majumdar, Dr S Woolner

18 December 2026 PhD Research Project Competition Funded PhD Project (Students Worldwide)

Nonlinear internal waves under ice (PARAUE_U27SCI)

University of East Anglia

School of Mathematics

Primary supervisor - Prof Emilian Parau. Internal waves occur in many stratified oceans, including ice-covered regions of the Arctic and Antarctic. Read more

Supervisor: Prof E Parau

24 February 2027 PhD Research Project Competition Funded PhD Project (UK Students Only)

Accelerating Chemical Process Development via Uncertainty-Aware Modelling and Experimental Design

The University of Manchester

Department of Mathematics

AI_CDT_DecisionMaking. Details. Chemical processes are essential to medicines, materials and clean energy but are complex and difficult to scale. Read more

Supervisors: Dr T Waite, Prof S Kaski, Dr J Zhang

4 December 2026 PhD Research Project Competition Funded PhD Project (Students Worldwide)

Designing ensembles for efficient climate model emulation and uncertainty quantification

University of Exeter

Mathematics and Statistics

Background. As climate change outpaces current mitigation frameworks, the strategic design of adaptation policies becomes increasingly crucial. Read more

Supervisors: Prof P Challenor, Dr H Mohammadi

13 January 2027 PhD Research Project Competition Funded PhD Project (Students Worldwide)

[School of Natural Sciences PhD Scholarships] Geophysical fluid mechanics: Modelling debris flows

The University of Manchester

Department of Mathematics

Debris flows are complex mixtures of water, boulders, rock, soil, wood, etc, that develop on steep slopes and travel long distances, destroying houses, roads, railways and other infrastructure, as well as killing people that are caught up in them. Read more

Supervisors: Prof N Gray, Dr C Johnson

Year round applications PhD Research Project Competition Funded PhD Project (Students Worldwide)

[School of Natural Sciences PhD Scholarships] The influence of nonlinear behaviour between different models of fluid flows

The University of Manchester

Department of Mathematics

Many problems in fluid mechanics can be investigated by using reduced models. In recent years, the trend has been to use neural networks or other model reduction techniques to learn solutions from high-resolution computations of the full-field equations, e.g. Read more

Supervisors: Prof A Hazel, Prof R E Hewitt

Year round applications PhD Research Project Competition Funded PhD Project (Students Worldwide)

[School of Natural Sciences PhD Scholarships] Joint Modelling of Longitudinal Outcomes and Multistate Survival Processes for Dynamic Prediction of Disease Progression

The University of Manchester

Department of Mathematics

Longitudinal studies in health and ageing research routinely collect repeated measurements of health outcomes alongside information on changes in clinical and functional status. Read more

Supervisors: Dr T Baghfalaki, Dr AM Maharani

Year round applications PhD Research Project Competition Funded PhD Project (Students Worldwide)

[School of Natural Sciences PhD Scholarships] Distributional Approximation by Stein's Method

The University of Manchester

Department of Mathematics

Stein's method is a powerful (and elegant) technique for deriving bounds on the distance between two probability distributions with respect to a probability metric. Read more

Supervisors: Dr R Gaunt, Dr D Denisov

Year round applications PhD Research Project Competition Funded PhD Project (Students Worldwide)

[School of Natural Sciences PhD Scholarships] The Fluid Mechanics of Particle Segregation

The University of Manchester

Department of Mathematics

Coffee, breakfast cereal and sand and gravel are common examples of granular materials that we encounter in our everyday lives, but they are used extensively by industry in the manufacture of nearly everything that we use. Read more

Supervisors: Prof N Gray, Dr C Johnson

Year round applications PhD Research Project Competition Funded PhD Project (Students Worldwide)

[School of Natural Sciences PhD Scholarships] Large-data limits in Markov chain Monte Carlo

The University of Manchester

Department of Mathematics

We typically employ Bayesian inference in cases where, in addition to parameter inference, we are interested in quantifying the uncertainties that remain in the parameter after the data observation. Read more

Supervisors: Dr JL Latz, Dr T Waite

Year round applications PhD Research Project Competition Funded PhD Project (Students Worldwide)

[School of Natural Sciences PhD Scholarships] Geometry of numbers beyond lattices

The University of Manchester

Department of Mathematics

The geometry of numbers studies the remarkable interplay between arithmetic and geometry through lattices. But how much of this theory really depends on lattices being groups?. Read more

Supervisors: Dr Y Smilansky, Dr D Robertson

Year round applications PhD Research Project Competition Funded PhD Project (Students Worldwide)

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