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This webpage describes the application process for the Centre for Doctoral Training in Algebra, Geometry, and Quantum Fields, a joint initiative of Heriot-Watt University, the University of Edinburgh, and the University of Glasgow. Applicants will also be considered for the following closely aligned degree programmes:

  • PhD in Algebra, Geometry and Topology, at the University of Edinburgh
  • PhD in Mathematical Physics, at the University of Edinburgh
  • PhD in Mathematics, at the University of Glasgow

The deadline for full consideration is 19 December 2025, for a September 2026 start.   Applications received after this date will be processed and considered on a rolling basis until all funding for 26/27 entry has been allocated.  See the Frequently Asked Questions for a more detailed timeline.

Students must submit both Pre-Application and Application webforms.

The details collected will be shared across the three AGQ universities: Heriot-Watt University, the University of Edinburgh, and the University of Glasgow.

The application process consists of four steps:

  • 1: Pre-application

    Fill out a pre-application webform at the link below. It is important that you review the instructions on this page before submitting the Pre-application webform. 

    Pre-application

    Please apply by 19th December 2025 for full consideration (applications will be processed and considered on a rolling basis after that).

  • 2: Application

    Submit a follow-up full application to the University of Glasgow’s admissions portal.  We stress that this portal will collect application data for all the above degree programmes, at all three universities.  

    It is important that you review the instructions on this page before submitting the application webform. 

    Application

    Please apply by December 19th for full consideration (applications will be processed and considered on a rolling basis after that)

  • 3: Letters of reference

    Arrange two academic letters of reference to be submitted by 9th January, 2026.

    Please email each of your referees and ask them to submit their letters of recommendation to the AGQ CDT at the following weblink: 

    https://www.agq-cdt.org/submit-reference

  • 4: Interviews

    Interviews will begin in February. 

On the pre-application webform, you will be asked to provide:

  • Your preference of admissions panel (see below).
  • A choice of three keywords which describe your mathematical interests.
  • A half-page statement (1000 characters, at most) describing a piece of academic work you are proud of, and explain why you are proud of it, with the option to attach it in pdf form, if applicable. 
  • A half-page answer (1000 characters, at most) to the question: “Why are you applying to undertake graduate studies in mathematics?”.
  • Your preferred supervisor(s), if any.  This is completely optional, and will be withheld from admissions panels, however it will be shared at the stage of arranging interviews.
  • The name and email address of two referees who will provide a reference letter in support of your application.
  • Whether you would like to be considered for an MSc. pre-year scholarship.  Your answer to this question will be withheld from admissions panels, so it will not bias in either direction your admissions decision into the PhD programme.
  • Demographic data.  This information will not be made available to admissions panels, nor during interviews.  It will only be used confidentially by the CDT Executive Team, and reported in aggregate to UKRI and other funders, for the purpose of ensuring equity and fairness in our admissions process.

The admissions panels and their members are:

  • Algebra and category theory
    Clark Barwick, Sjoerd Beentjes, Gwyn Bellamy, Iain Gordon, David Jordan, Mark Lawson, Darrick Lee, Tom Leinster, Dinakar Muthiah, Jon Pridham, Anna Puskás, Pavel Safronov, Christian Sämann, Alexander Shapiro, Sue Sierra, and Agata Smoktunowicz,.
  • Geometric group theory, low-dimensional topology and algebraic topology
    Jim Belk, Rachael Boyd, Tara Brendle, Laura I Ciobanu Radomirovic, Matthew Cordes, Ana Garcia Lecuona, Alexandre Martin, Brendan Owens, Mark Powell, and Alessandro Sisto.
  • Algebraic/complex/symplectic geometry, and number theory
    Alex Bartel, Arend Bayer, Ivan Cheltsov, Ben Davison, Damián Gvirtz-Chen, Milena Hering, Minhyong Kim, Antony Maciocia, Johan Martens, Ana Rita Pires, Nick Sheridan, Efthymios Sofos, Andy Wand, and Michael Wemyss.
  • Theoretical physics
    Latham Boyle, Einan Gardi, Anton Ilderton, Davide Micheletto, Tyler Shendruk, and Neil Turok.
  • Mathematical physics
    Tim Adamo, Murad Alim, Theo Assiotis, Richard Davison, Tudor Dimofte, Anastasia Doikou, Misha Feigin, José Miguel Figueroa-O’Farrill, James Gaunt, Claire Gilson, Jelle Hartong, Lotte Hollands, Anton Izosimov, Christian Korff, Anatoly Konechny, Jules Lamers, James Lucietti, Bernd Schroers, Joan Simón, Ian Strachan, Richard Szabo, Sayantani Bhattacharyya, Matthew Walters, and Robert Weston.
  • Operator algebras and dynamics
    Vaibhav Gadre, Xin Li, Christian Voigt, Mike Whittaker, Runlian Xia, and Joachim Zacharias.
  • No panel
    Choose this option if you are unable to determine the best panel for your application.  In this case we will assign you to a panel that most closely suits your interests and coursework.

Your application will be available to all supervisors, not only those on your admissions panel, however the admissions panel will provide the first pass over your application.  It may be helpful to peruse the supervisor page to get an idea of the panelists’ interests.

You will then be directed to the University of Glasgow’s admissions portal, in order to provide:

  • Transcripts, in pdf form
  • A CV, in pdf form

Some applicants from outside the United Kingdom may be required to provide evidence of proficiency in the English language. Details on this requirement can be found in the Frequently Asked Questions section below. 

If any of your transcripts are in a language other than English you will be required to provide certified translations.

Application Instructions

While the instructions on the Glasgow application portal are self-evident in most cases, there are a few questions that require you to enter information specific to this process. Please follow the instructions below: 

  • 1 . On the ‘Application Homepage’

    Please insert September 1, 2026 as the Proposed Start Date.

  • 2. On the ‘Finances’ page: 
    • For the question: ‘How do you intend to fund your studies at the University of Glasgow?’ answer: ‘University of Glasgow Scholarship’ 
    • For the question: ‘If you are applying or have secured funding please provide details eg. Scholarship name’ answer: ‘N/A’
    • For the question: ‘Is this funding confirmed?’ answer ‘No’
  • 3. On the ‘References’ page:

    If you have your reference documents already you can upload a pdf copy of two references. If you do not have a pdf copy (many applicants will not have a pdf copy as these are customarily held in confidence) please enter the information below in this section of the application:

    Referee One:
    First Name: Not applicable
    Last Name: Not applicable
    Email: agq-references@glasgow.ac.uk
    Capacity in which you know the referee: Not applicable

    Referee Two:
    First Name: Not applicable
    Last Name: Not applicable
    Email: agq-cdt@glasgow.ac.uk
    Capacity in which you know the referee: Not applicable


    Please note: 

    We will be collecting references separate from this application system, as described above.  For this reason, please do not re-enter your reference writer’s details (which would result in them receiving an irrelevant automated email), and instead follow the instructions above.

  • 4. On the ‘Research’ page: 
    • For the question about your supervisor please select Professor Tara Brendle.  
    • For the field ‘You are restricted to 250 characters in this field, please use the upload if required’ please enter the name of the admissions panel you selected on the Pre-Application form. 
    • For the question: ‘Have you contacted the Supervisor?’ answer: ‘No’

    Please note: you are asked to indicate Professor Tara Brendle here, although you may have entered other colleagues in the pre-application.  The Glasgow admissions portal does not contain the name of all supervisors, and so we will refer only to the pre-application form for the (optional) indication of a preferred supervisor.

    • You can leave the Research Proposal section blank. A research proposal is not required for this application. 
  • 5. On the ‘Supporting Documents’ page:  
    • For the ‘Bachelor transcript / mark sheets (official document detailing modules / courses taken and grades so far)’. You must upload a transcript that shows the marks you have obtained during your studied for each individual course. If you have not completed your degree, please include a transcript showing the marks you have so far.  
    • For the ‘Curriculum Vitae’ upload a CV that provides information about your background and professional experience, especially when it comes to aspects that you think make you a good candidate for graduate study in mathematics.

Frequently Asked Questions

Applicants must have or expect to have of a at least a 2.1 degree or the international equivalent.  

Students who apply will be considered for both the PhD in Algebra, Geometry and Quantum Fields as well as the pre-year MSc program which serve as an admissions pathway to the PhD.

CDT stands for Centre for Doctoral Training (CDT) and is one of the approaches used by Engineering and Physical Science Research Council (EPSRC) to fund and train doctoral students across the UK. CDTs focus on cohort-based learning experiences and skills training to develop a future academic or industry career. They are funded by research councils which fall under the umbrella of UK Research and Innovation.

The AGQ CDT 2026/2027 admissions timeline, including important dates, is provided below for your reference.

The AGQ CDT is a fully funded PhD program, covering four years of tuition fees and an annual stipend that is currently set at £19,132 for the 2024/25 academic year (increasing yearly with the UKRI stipend rate). A stipend is a tax-free payment to support students to pay living costs and the basic expenses associated with study. 

 

Applicants from outside the United Kingdom may be required to provide evidence of proficiency in the English language.  Applicants must have one of the following qualifications as evidence of their English language ability:
  • an undergraduate or masters degree, that was taught and assessed in English in a majority English speaking country as defined by UK Visas and Immigration
  • Accepted English Proficiency Tests include:
    • IELTS Academic: total 6.5 with at least 6.0 in each component
    • TOEFL-iBT: total 92 with at least 20 in each section
    • PTE(A): total 68 with at least 63 in each section
    • CAE and CPE: total 176 with at least 169 in each paper
    • Trinity ISE
    • OET
  • All English Proficiency Tests must have been awarded within two years at the point of application.
  • For additional information on specific English Language requirements please contact the central Glasgow University admissions team using this webform.

Our students’ primary institution is the same as their principal supervisor’s, however all teaching is hybrid and joint between the three institutions, and the degree is awarded jointly by all three institutions. Applications will be considered by multiple supervisors at the same institution, as well as being considered across all institutions. Applicants can receive multiple offers from different supervisors at different institutions.

Your application can still be reviewed if you are missing some evidence, however having full information available to the admissions panel will strengthen your application. If you are interviewed and offered a position with the CDT, this offer will be conditional that all above evidence requirements are satisfied.

The pre-year MSc programme is fully funded in the same manner as the PhD, with fees covered and a stipend paid to students.

Please email admissions@agq-cdt.org for further queries.

Admissions to a PhD programme is a very complicated process.  We aim to complete the first round of admissions by June, however we may run a secondary round after that if additional funding opportunities arise.

If you have a competing offer with a deadline, you may write to admissions@agq-cdt.org with the deadline, and to request an update.  We will try our best to give you timely information under these circumstances.

However, please note that due to the volume of inquiries we cannot respond to individual requests for general updates.  Instead, we have created the page https://www.agq-cdt.org/admission-status where we will post general updates about the admissions process.