Postgraduate study

Geometry and Topology PhD

Awards: PhD

Funding opportunities

Programme website: Geometry and Topology

Our research group has strong links with both the Algebra & Number Theory and the Mathematical Physics research groups. You’ll find these invaluable, as opportunities to discuss your work and expand your thinking abound.

The School of Mathematics is a vibrant community of more than 60 academic and related staff supervising 60 students.

Working within one of the largest mathematics groups in the UK, you’ll be completing your degree in an environment that hums with a busy graduate school life, and you’ll have the chance to make your mark in seminars, workshops, clubs and outings.

The Hodge Institute is the home of algebra, geometry, number theory and topology research groups in the School of Mathematics.

Our interests include:

  • algebraic geometry
  • derived categories
  • algebraic and geometric topology
  • twistor theory
  • category theory
  • integrable systems

While we can offer a large community of researchers under one roof, we believe in encouraging you to gain as broad a perspective as possible. The best way to do this is to involve yourself in the international dialogue on your research area, through attending conferences and symposia, and visiting your peers in centres of research worldwide. Throughout your studies, you’ll be given opportunities to travel to events and institutions that will allow you to gain this perspective, and open up new areas of investigation.

Mathematics is a discipline of high intellect with connections stretching across all the scientific disciplines and beyond, and in Edinburgh you can be certain of thriving in a rich academic setting. Our School is one of the country’s largest mathematics research communities in its own right, but you will also benefit from Edinburgh’s high-level collaborations, both regional and international.

Research students will have a primary and secondary supervisor and the opportunity to network with a large and varied peer group. You will be carrying out your research in the company of eminent figures and be exposed to a steady stream of distinguished researchers from all over the world.

Our status as one of the most prestigious schools in the UK for mathematics attracts highly respected staff. Many of our 60 current academics are leaders in their fields and have been recognised with international awards.

Researchers are encouraged to travel and participate in conferences and seminars. You’ll also be in the right place in Edinburgh to meet distinguished researchers from all over the world who are attracted to conferences held at the School and the various collaborative centres based here. You’ll find opportunities for networking that could have far-reaching effects on your career in mathematics.

You will enjoy excellent facilities, ranging from one of the world’s major supercomputing hubs to generous library provision for research at the leading level, including the new Noreen and Kenneth Murray Library at King’s Buildings.

Students have access to more than 1,400 computers in suites distributed across the University’s sites, many of which are open 24 hours a day. In addition, if you are a research student, you will have your own desk with desktop computer.

We provide all our mathematics postgraduates with access to software packages such as Maple, Matlab and Mathematica. Research students are allocated parallel computing time on ‘Eddie’ – the Edinburgh Compute and Data Facility. It is also possible to arrange use of the BlueGene/Q supercomputer facility if your research requires it.

A UK first class honours degree, or its international equivalent, in an appropriate subject; 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

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

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

  • TOEFL-iBT: total 92 with at least 20 in each section

  • PTE Academic: total 61 with at least 56 in each of the Communicative Skills scores

  • CAE and CPE: total 176 with at least 169 in each paper

  • Trinity ISE: ISE II with distinctions in all four components

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, PTE Academic or Trinity ISE, 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.

If you are not a national of a majority English speaking country, then your degree must be no more than three and a half years old at the beginning of your programme of study.*

(*Revised 8/11/2018 to provide more accurate information on English language qualifications expiry dates. Revised 22/03/2019 to provide more accurate/comprehensive information.)

Find out more about our language requirements:

Read our general information on tuition fees and studying costs:

Featured funding

UK government postgraduate loans

If you live in the UK, you may be able to apply for a postgraduate loan from one of the UK’s governments. The type and amount of financial support you are eligible for will depend on your programme, the duration of your studies, and your residency status. (Programmes studied on a part-time intermittent basis are not eligible.)

Other funding opportunities

Search for scholarships and funding opportunities:

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

We strongly recommend you submit your completed application as early as possible, particularly if you are also applying for funding or will require a visa. We may consider late applications if we have places available.

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

Further information

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