Postgraduate study
Edinburgh: Extraordinary futures await.

Centre for Doctoral Training in Algebra, Geometry and Mathematical Physics PhD with Integrated Study

Awards: PhD with Integrated Study

Study modes: Full-time, Part-time

Funding opportunities


The Centre for Doctoral Training (CDT) in Algebra, Geometry and Mathematical Physics aims to train graduate students to research excellence in diverse disciplines, such as:

  • pure mathematics
  • mathematical and theoretical physics, including:

    • algebra
    • geometry
    • topology
    • quantum field theory
    • gauge theory
    • gravity

You will navigate the many vibrant interfaces among these disciplines, learning to communicate ideas fluently across different areas of mathematics and physics, and harnessing the power of interfaces to advance research.

You will incorporate advanced computing methods in your research and will have the opportunity to work with some of our 30+ partners in the international academic community, industry, and the third sector.

You will train together in cohorts, combining multiple disciplines and backgrounds. You will be supported to work on short group projects and to participate in a variety of activities to enhance your mathematical/scientific breadth and communication skills.

As part of the structure of our PhD with integrated studies, you must study taught courses while completing the research elements of a traditional PhD programme.

We have designed the programme to be flexible in the way credits are acquired. However, you must successfully complete 180 taught credits over the first 3 years, plus the equivalent of 3 years of PhD research, spread over the 4-year programme.

The 180 taught credits consist of:

  • 30 credits of mandatory cohort activities in Year 1 including a group project
  • 30 credits of advanced computing coursework and a computing project in Year 2
  • 30 credits from an internship/placement during the Year 3

The remaining 90 credits can be accrued in Years 1-2 by completing six courses from a broad selection offered across algebra, geometry, mathematical physics, and their interfaces; and/or participating in approved reading groups or seminars.

Every student will have a placement during Year 3, lasting approximately 3 months. During the placement, you will use and expand skills developed during their CDT training. The placements will involve working with one of our partners, either:

  • as a visitor in another academic research group
  • in industry, with a variety of companies connecting mathematics and physics with data and technology
  • in the third sector, e.g. engaging in outreach in the UK or internationally

As part of a new cohort-based training centre, students will receive extensive additional training beyond their thesis research, with emphasis on communication and leadership skills as well as research computing skills.

You will be part of a world-class and interdisciplinary research community at the University of Edinburgh as well as our partner institutions, Heriot-Watt University and the University of Glasgow (where there will also be students participating in the CDT cohort).

You will have access at all three institutions facilities, including:

  • common meeting and study space
  • participation in research seminars, with a wide array of international visitors.

They will also be able to participate virtually in activities at the different institutions.

Students enrolled in the CDT at the University of Edinburgh will have dedicated desk space in Year 1 in the state-of-the-art Bayes Centre, where many cohort activities will take place); and in Years 2-4 in the James Clerk Maxwell Building.

Graduates on this degree will be well-prepared to find employment and to become leaders in a diverse array of industries, including:

  • academia and research
  • industrial sectors, including:

    • tech
    • finance
    • consultancy
    • cryptography and security
    • quantum technologies
  • third sectors, including:

    • public engagement
    • government
    • policy
    • education

These entry requirements are for the 2024/25 academic year and requirements for future academic years may differ. Entry requirements for the 2025/26 academic year will be published on 1 Oct 2024.

A UK first class honours degree, or its international equivalent, in an appropriate subject related to the CDT; or a UK 2:1 honours degree plus a UK masters degree, or their international equivalents; or relevant qualifications and experience.

International qualifications

Check whether your international qualifications meet our general entry requirements:

English language requirements

Regardless of your nationality or country of residence, you must demonstrate a level of English language competency at a level that will enable you to succeed in your studies.

English language tests

We accept the following English language qualifications at the grades specified:

  • IELTS Academic: total 6.5 with at least 6.0 in each component. We do not accept IELTS One Skill Retake to meet our English language requirements.
  • TOEFL-iBT (including Home Edition): total 92 with at least 20 in each component. We do not accept TOEFL MyBest Score to meet our English language requirements.
  • C1 Advanced (CAE) / C2 Proficiency (CPE): total 176 with at least 169 in each component.
  • Trinity ISE: ISE II with distinctions in all four components.
  • PTE Academic: total 62 with at least 59 in each component.

Your English language qualification must be no more than three and a half years old from the start date of the programme you are applying to study, unless you are using IELTS, TOEFL, Trinity ISE or PTE, in which case it must be no more than two years old.

Degrees taught and assessed in English

We also accept an undergraduate or postgraduate degree that has been taught and assessed in English in a majority English speaking country, as defined by UK Visas and Immigration:

We also accept a degree that has been taught and assessed in English from a university on our list of approved universities in non-majority English speaking countries (non-MESC).

If you are not a national of a majority English speaking country, then your degree must be no more than five years old* at the beginning of your programme of study. (*Revised 05 March 2024 to extend degree validity to five years.)

Find out more about our language requirements:

Read our general information on tuition fees and studying costs:

The CDT will be seeking to fund approx. 8 studentships for each cohort, with up to a further 8 through matched and other funding sources, with the ambition to create diverse cohorts of students from different backgrounds and disciplines.

Studentship funding may be subject to eligibility requirements as set by the programme funder. We will conduct eligibility assessments as part of the application process and applicants will be automatically considered for studentship funding.

Search for scholarships and funding opportunities:

  • Mathematics Graduate School
  • James Clerk Maxwell Building
  • Peter Guthrie Tait Road
  • The King's Buildings Campus
  • Edinburgh
  • EH9 3FD

Applications received before the deadline will receive full consideration. Applications received after the deadline will be considered in a rolling fashion until places are filled.

You must submit an application via the EUCLID application portal and provide the required information and documentation. This will include submission of: *a Curriculum Vitae (CV)

  • degree certificates and official transcripts of all completed and in-progress degrees (plus certified translations if academic documents are not issued in English)
  • two academic references

Only complete applications will progress forward to the academic selection stage.

Find out more about the general application process for postgraduate programmes:

Further information

  • Mathematics Graduate School
  • James Clerk Maxwell Building
  • Peter Guthrie Tait Road
  • The King's Buildings Campus
  • Edinburgh
  • EH9 3FD