Centre for Doctoral Training in Algebra, Geometry and Quantum Fields PhD
University of Edinburgh , United Kingdom
Centre for Doctoral Training in Algebra, Geometry and Quantum Fields PhD with Integrated Study
University of Edinburgh
Mathematics and Mathematical Physics
Program Overview: CDT in Algebra, Geometry and Quantum Fields
The Centre for Doctoral Training (CDT) in Algebra, Geometry and Quantum Fields is an EPSRC-funded collaborative PhD programme spanning three leading Scottish universities: the University of Edinburgh, the University of Glasgow, and Heriot-Watt University. This innovative programme trains graduate students to research excellence in diverse disciplines including algebra, geometry, topology, mathematical physics, and quantum field theory.
As a doctoral researcher, you will navigate the vibrant interfaces among these disciplines, learning to communicate ideas fluently across different areas of mathematics and physics while harnessing the power of interdisciplinary approaches to advance research. You will incorporate advanced computing methods in your research and have the opportunity to work with over 30 partners in the international academic community, industry, and the third sector.
Students train together in cohorts, combining multiple disciplines and backgrounds, and are supported to work on short group projects and participate in activities that enhance mathematical breadth and communication skills. The programme also includes a three-month placement in Year 3 with an industry, academic, or third-sector partner, preparing graduates for leadership roles in academia, industry, and society.
Key Program Highlights
- Collaborative CDT across three leading Scottish universities with 60+ internationally esteemed supervisors
- Cohort-based training with emphasis on communication, leadership, and research computing skills
- Three-month industry, academic, or third-sector placement integrated into the programme
- Advanced computing training in machine learning, symbolic computing, and AI-assisted proofs
Curriculum and Research Training Structure
The CDT programme combines traditional PhD research with integrated taught courses and professional development. Students take up to six courses from a broad selection across algebra, geometry, mathematical physics, and their interfaces, while pursuing cutting-edge thesis projects supervised by the centre's pool of 60+ internationally recognised researchers.
Algebra and Category Theory
15 creditsAdvanced topics in algebraic structures, category theory, and their applications, covering areas such as higher algebra, representation theory, and homological methods at the forefront of modern mathematical research.
Algebraic, Complex, and Symplectic Geometry
15 creditsExploration of geometric structures including algebraic geometry, complex manifolds, and symplectic geometry, with connections to mirror symmetry and number theory.
Mathematical Physics and Quantum Field Theory
15 creditsStudy of the mathematical foundations of quantum field theory, gauge theory, string theory, and gravity, bridging pure mathematics and theoretical physics.
Geometric Group Theory and Topology
15 creditsAdvanced topics in geometric group theory, low-dimensional topology, algebraic topology, and their interactions with other areas of mathematics.
Advanced Research Computing
15 creditsTraining in advanced computational methods including machine learning, symbolic computing, computer algebra, and AI-assisted proofs, equipping students to integrate modern computing tools into their research.
Doctoral Thesis Research
Ongoing across Years 1-4Original research conducted under the supervision of leading academics, culminating in a doctoral thesis that makes a significant contribution to knowledge in algebra, geometry, quantum fields, or their interfaces.
Elective Courses and Reading Groups
Admission Requirements
The CDT in Algebra, Geometry and Quantum Fields seeks highly motivated candidates with strong backgrounds in mathematics or mathematical physics. All applications are processed through Uni4Edu, and applicants are automatically considered for studentship funding as part of the admissions process.
Academic Requirements
- Primary Academic RequirementA UK first class honours degree, or its international equivalent, in mathematics, mathematical physics, or a closely related subject
- Alternative Academic PathwayA UK 2:1 honours degree plus a UK masters degree, or their international equivalents, in a relevant subject
- Research ReadinessCandidates should typically have a good understanding of the field they propose to study, with some research experience preferred
- Pre-Year MSc PathwayApplicants may also be considered for a fully funded pre-year MSc programme serving as an admissions pathway to the PhD
- Supervisor IdentificationStudents are encouraged to identify research interests and potential supervisors, though it is not essential to have secured a supervisor before applying
English Language Requirements
- IELTS AcademicTotal 6.5 with at least 6.0 in each component
- TOEFL iBTTotal 92 with at least 20 in each section (pre-January 2026 scoring)
- Cambridge C1 Advanced (CAE) / C2 Proficiency (CPE)Total 176 with at least 169 in each component
Required Documents
Application Deadlines
For personalized admission guidance, document verification, and application support, please contact Uni4Edu
Scholarships and Funding
The CDT in Algebra, Geometry and Quantum Fields is an EPSRC-funded programme, and most PhD students in Mathematics at Edinburgh receive full scholarships. The CDT seeks to fund approximately 8 studentships per cohort, with up to a further 8 through matched and other funding sources. All applicants are automatically considered for studentship funding as part of the application process.
EPSRC CDT Studentship
Full funding covering tuition fees and annual stipend for four yearsThe primary funding source for AGQ CDT students, provided by the Engineering and Physical Sciences Research Council (EPSRC). This covers tuition fees and provides an annual living stipend at the UKRI rate. Eligibility requirements may apply as set by the programme funder.
Pre-Year MSc Funding
Full funding covering tuition fees and stipend for the pre-yearStudents admitted through the pre-year MSc pathway receive fully funded support in the same manner as PhD students, with fees covered and a stipend provided during the preparatory masters year.
Matched and Partner Funding
Varies by funding sourceAdditional studentships funded through matched contributions from university partners and external sources. Contact Uni4Edu for details on current availability and eligibility for these additional funding opportunities.
For detailed tuition fee information, please contact Uni4Edu — we will guide you through the costs and available funding options for this program.
Career Prospects and Outcomes
Graduates of the CDT in Algebra, Geometry and Quantum Fields are equipped with advanced mathematical expertise, leadership skills, and practical experience through industry placements. The programme prepares graduates for careers in academia, industry, and the wider public sector, with particular strengths in sectors where mathematical sciences drive innovation including computing, quantum technologies, finance, and cryptography.
Potential Career Paths
Sectors and Employers Hiring Graduates
Rankings and Recognition
The University of Edinburgh is consistently ranked among the top universities in the world and is recognised for its exceptional research power and academic reputation. Founded in 1583, Edinburgh is one of the UK's most prestigious institutions, ranked 4th in the UK for research power based on the 2021 Research Excellence Framework.
| Subject | Ranking Body | Rank |
|---|---|---|
| Mathematics | QS World University Rankings by Subject | Top 50 (contact Uni4Edu for current data) |
| Research Power (Overall) | Research Excellence Framework (REF) | #4 in the UK |
| Natural Sciences | QS Faculty Rankings | Top 50 (contact Uni4Edu for current data) |
| Physical Sciences | THE World University Rankings by Subject | Top 50 (contact Uni4Edu for current data) |
How to Apply
Applying for this program is easy with Uni4Edu. Our team will guide you through every step of the process — from document preparation to final enrolment.
Contact Uni4Edu
Reach out to our team via email or phone. We will assess your profile and confirm your eligibility for this program.
Prepare Your Documents
Our advisors will provide you with a personalised checklist of required documents and help you prepare your application package.
Submit Your Application
Uni4Edu will submit your application on your behalf and keep you updated on its progress throughout the review period.
Receive Your Offer
Once accepted, we will help you understand your offer, arrange visa support if needed, and guide you through the enrolment process.
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