About the Project
This project will be focussed within Algebraic Number Theory and centred around questions arising from Diophantine equations, modular forms, and elliptic curves and involve a blend of algebraic, analytic and computational methods.
This project is expected to start in September 2027.
Before you apply: We strongly recommend that you contact the supervisors for this project before you apply.
How to apply: To be considered for this project you must complete a formal application through our online application portal. If you already have an applicant account this link will directly open an application for PhD School of Natural Sciences Scholarships. If you don’t already have an applicant account, please follow the instructions here.
When applying, please specify the full title and supervisor/s of the project, details of your previous study, and names and contact details of two referees. You must also upload a Supporting Statement describing your motivation to apply to the project, your CV and transcripts of awarded and in-progress university qualifications. Please note late or incomplete applications will not be considered.
Equality, diversity and inclusion are fundamental to the success of The University of Manchester and central to all our activities. A diverse research community strengthens creativity, productivity and quality, while increasing the societal and economic impact of our work. We welcome applicants from all career paths, backgrounds and sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation or transgender status.
We welcome applications from candidates returning to study after a career break or experience in other roles. Flexible study arrangements may be available, including part-time study at 50%, 60% or 80%, subject to the requirements of the project and funder.
Eligibility: The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree (or international equivalent) in Mathematics OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) in Mathematics. Undergraduate and Masters courses covered must include: Algebraic Number Theory, Galois Theory, Elliptic Curves, Modular Forms as well as other advances courses in Algebra and Number Theory.
This project will remain open until filled.
If your application is submitted by 1st November 2026, you can expect a decision by 18th December 2026.
If your application is submitted by 15th January 2027, you can expect a decision by 30th March 2027.
Self or externally funded students can also be considered for this project.
FSE_SoNS
Funding Notes
Funding covers tuition fees, an annual stipend at the UKRI minimum rate (currently £21,805 per year), and a research training support grant of up to £2,500 per year for the full 3.5-year programme.