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mathematics PhD Projects, Programmes & Scholarships

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

[School of Natural Sciences PhD Scholarships] Differential algebra and the model theory of differential equations

The University of Manchester

Department of Mathematics

Differential algebra studies differential equations using algebraic methods, treating differentiation as an operation on a field. Read more

Supervisors: Dr V Aslanyan, Dr O Sanchez

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

[School of Natural Sciences PhD Scholarships] Statistical inference of transmission chains or outbreaks

The University of Manchester

Department of Mathematics

There are increasingly established statistical inference tools for fitting epidemic models to data from traditional MLE methods to MCMC to STAN. Read more

Supervisors: Prof I Hall, Dr T House

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

[School of Natural Sciences PhD Scholarships] Bayesian Monte Carlo Methods for Complex Generative Time-Series Models

The University of Manchester

Department of Mathematics

Time series arise throughout finance, economics science and technology, and are increasingly modelled using sophisticated generative systems. Read more

Supervisors: Dr W Li, Dr N Guha

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

[School of Natural Sciences PhD Scholarships] Mixed-Precision Randomized Numerical Linear Algebra

The University of Manchester

Department of Mathematics

Modern scientific computing and data analysis increasingly involve matrices that are too large for traditional numerical algorithms to handle efficiently. Read more

Supervisors: Dr M Webb, Prof F Tisseur

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

[School of Natural Sciences PhD Scholarships] Surface topology, dynamics and groups

The University of Manchester

Department of Mathematics

This project will concern homeomorphisms and/or mapping class groups of surfaces, which can include for example the braid groups. Read more

Supervisors: Dr R Webb, Prof L Rempe

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

[School of Natural Sciences PhD Scholarships] Elastic particles in low Reynolds flows

The University of Manchester

Department of Mathematics

Many fluid mechanical problems involve the motion of thin/slender particles (such as elastic sheets or fibres) in low-Reynolds-number flows. Read more

Supervisors: Prof M Heil, Dr D Pihler-Puzovic

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

[School of Natural Sciences PhD Scholarships] Deflation Techniques for Optimization Algorithms

The University of Manchester

Department of Mathematics

Many optimization problems have a large number of local minima, making it difficult to identify the global minimum, or even a representative collection of good candidate solutions. Read more

Supervisors: Dr M Webb, Dr JL Latz

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

[School of Natural Sciences PhD Scholarships] Multiple-bubble interactions in Hele-Shaw cells

The University of Manchester

Department of Mathematics

The study of air bubbles and fingers in Hele-Shaw cells at low Reynolds number is an area with surprisingly rich dynamics, in terms of nonlinear dynamics, fluid mechanical modelling and experimental fluid mechanics. Read more

Supervisor: Dr A Thompson

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

[School of Natural Sciences PhD Scholarships] Tontines: diverse cohorts and automated adjustments

The University of Manchester

Department of Mathematics

The world faces an ongoing retirement crisis. Governments and insurance companies seek retirement products that cope with rising life expectancy and uncertain financial markets. Read more

Supervisor: Dr T Bernhardt

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

[School of Natural Sciences PhD Scholarships] Dynamic, individualised prediction of the kidney–heart cascade: multistate joint models for irregular primary care and hospital data

The University of Manchester

Department of Mathematics

Kidney disease and heart disease feed each other. Kidney function declines, cardiovascular risk rises, and a cardiovascular event or its treatment damages the kidneys further. Read more

Supervisor: Dr M Bhattacharjee

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

[School of Natural Sciences PhD Scholarships] Model Theory of ordered algebraic structures

The University of Manchester

Department of Mathematics

The aim in this project is to prove decidability of various fragments of the ring of functions of class C^k from the euclidean space to the real line, that are definable in the real field. Read more

Supervisors: Dr M Tressl, Dr O Sanchez

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

Beyond Pairwise Connections: Higher-Order Models of Human Brain Networks

University of Birmingham

School of Mathematics

Research Group: AMICO Lab

The human brain is commonly represented as a network in which brain regions are nodes and connections between pairs of regions are edges. Read more

Supervisors: Dr E Amico, Prof F Spill

Year round applications PhD Research Project Competition Funded PhD Project (UK Students Only)

The development of young children’s understanding of multi-digit numbers (Ref: LN/JB-SF1/2026)

Loughborough University

Mathematics Education Centre

Once children have become proficient in using small numbers, they are faced with new challenges as soon as numbers get bigger. One of these challenges concerns the place-value structure of multi-digit numbers. Read more

Supervisor: Dr J Bahnmüller

7 January 2027 PhD Research Project Self-Funded PhD Students Only

Nonlinear systems of PDE and vectorial Calculus of Variations in L∞ (L-infinity)

University of Reading

Department of Mathematics and Statistics

The calculus of variations is, roughly speaking, the mathematical theory of how to minimise or maximise magnitudes. Variational problems from science typically require minimisation of an average magnitude over a space-time region depending on unknown quantities. Read more

Supervisor: Dr N Katzourakis

Year round applications PhD Research Project Self-Funded PhD Students Only

Active Room Acoustics with Microphone and Loudspeaker Arrays (with L-Acoustics)

University of Southampton

EPSRC Centre for Doctoral Training in Sustainable Sound Futures

Array-Based Architectures for Sustainable Active Acoustics Systems. Project Summary. What if a concert hall could change its acoustics electronically, adapting from speech to chamber music or a symphony, without requiring extensive architectural modifications?. Read more

Supervisors: Prof F Fazi, Prof P Nelson

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

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