Algebra, Geometry and Topology PhD Level: Postgraduate research Subject: Mathematics and Statistics Year of entry: 2026 Study options Full-time PhD | 4 years | Start date: September 2026 PhD with Internship | 4 years | Start date: September 2026 Key facts School School of Mathematics College College of Science and Engineering Programme website AGQ CDT website PhD by Distance Not available School location Multiple campuses Apply now 19 to 21 November 2025: Postgraduate Virtual Open Days Join us live to explore postgraduate taught and research study at Edinburgh and gain key insights before you apply. Register now Overview About the degree programme This programme is delivered by the Algebra, Geometry and Quantum Physics (AGQ) Centre for Doctoral Training, which spans across 3 leading Scottish universities: the University of Glasgow, Heriot-Watt University and the University of Edinburgh.On this programme, you must take taught courses while completing the research elements of a traditional PhD programme.The AGQ Centre for Doctoral Training (CDT) aims to train graduate students to research excellence in diverse disciplines, such as:pure mathematicsmathematical and theoretical physics, including:algebrageometrytopologyquantum field theorygauge theorygravityYou 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.Find out more about this programme on the AGQ websiteWorking 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.The Hodge Institute is the home of algebra, geometry, number theory and topology research groups in the School of Mathematics.The Hodge Institute Find out what it's like studying for a PhD in the School of Mathematics. Hear from some of our current PhD students as they share their experience of researching mathematics. Study options This programme is available with or without an internship requirement.Both of these programme options are available to study on a full-time basis (over 4 years) or a part-time basis (over 8 years). Applying How to apply See the AGQ website for information on how to apply.The application timeline is different to the University of Edinburgh's, as the start date for applications is typically in mid-October. When to apply Deadline for applications for 2026 entry: 19 December 2025 Application fee There is no fee to apply to this programme. Apply Apply online through the AGQ CDT website. Funding, fees and costs Funding Most PhD students in Mathematics receive full scholarships to cover their tuition fees and living costs.Others may use a combination of the following funding to pay their tuition fees and living costs:scholarshipsborrowing moneytaking out a loanfamily supportpersonal savingsincome from workemployer sponsorshipExplore sources of funding for postgraduate study Studentship fundingAll applicants will be automatically considered for studentship funding as part of the application process.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.The CDT seeks to fund approximately 8 studentships for each cohort, with up to a further 8 students funded through matched funding and other funding sources.School of Mathematics funding opportunitiesSchool of Mathematics funding opportunities Search for other funding opportunities You can find scholarships, bursaries and other funding you might be eligible for on our Scholarships and Student Funding site.Postgraduate funding opportunities Tuition fees Tuition fees by award and duration Tuition fees for full-time and part-time options are listed for one academic year. Full-time PhD (4 years) tuition fees PhD with Internship (4 years) tuition fees Graduate discount If you are a University of Edinburgh graduate, you will be eligible for a 10% discount on your tuition fees for this programme. You may also be eligible if you were a visiting undergraduate student.Find out how to receive your graduate discount Costs Accommodation and living costs You need to cover your accommodation and living costs for the duration of your programme.We estimate that you might spend £1,167 to £2,330 per month if you are a single student.Living costs include:foodutility billstravel, clothes, books and stationeryrecreational costs (for example, TV subscriptions and social events)Living costsAccommodation costs depend on where you live while studying and the type of accommodation you choose.University postgraduate accommodation options and costs Entry requirements These entry requirements are for the 2026-27 academic year and requirements for future academic years may differ. Entry requirements for the 2027-28 academic year will be published on 1 Oct 2026. Qualifications 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 To find international equivalent qualifications, select where you studied from the country or region list. Where you studied - Select a country or region -AfghanistanAlbaniaAngolaArgentinaArmeniaAustraliaAustriaAzerbaijanBahamasBahrainBangladeshBelarusBelgiumBelizeBeninBoliviaBosnia and HerzegovinaBotswanaBrazilBulgariaBurkina FasoBurundiCambodiaCameroonCanadaChileChinaColombiaCosta RicaCôte d'IvoireCroatiaCubaCyprusCzech RepublicDemocratic Republic of CongoDenmarkDominican RepublicEcuadorEgyptEl SalvadorEritreaEstoniaEswatiniEthiopiaFinlandFranceGabonThe GambiaGeorgiaGermanyGhanaGreeceGuatemalaGuineaHaitiHondurasHong Kong-SAR ChinaHungaryIcelandIndiaIndonesiaIranIraqIrelandIsraelItalyJamaicaJapanJordanKazakhstanKenyaKorea, Republic ofKuwaitLatviaLebanonLesothoLiberiaLibyaLithuaniaLuxembourgMacau-SAR ChinaMadagascarMalawiMalaysiaMaldivesMaliMaltaMauritiusMexicoMoldovaMongoliaMontenegroMoroccoMozambiqueMyanmarNamibiaNepalNetherlands, TheNew ZealandNicaraguaNigeriaNorth MacedoniaNorwayOmanPacific IslandsPakistanPalestinian TerritoriesPanamaParaguayPeruPhilippinesPolandPortugalQatarRomaniaRussiaRwandaSaudi ArabiaSenegalSerbiaSierra LeoneSingaporeSlovakiaSloveniaSomaliaSouth AfricaSouth SudanSpainSri LankaSudanSwedenSwitzerlandSyriaTajikistanTaiwanTanzaniaThailandTogoTrinidad and TobagoTurkeyTurkmenistanUgandaUkraineUnited Arab EmiratesUnited States of AmericaUruguayUzbekistanVenezuelaVietnamWest Indies and CaribbeanZambiaZimbabweMy country or region is not listed English language requirements You must prove that your English language abilities are at a high enough level to study this degree programme.This is the case for all applicants, including UK nationals.You can meet our English language requirements with one of the following:an English language testa degree that was taught and assessed in Englishcertain professional qualifications English language tests we accept We accept any of the following English language tests, at the specified grade or higher: 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. Oxford ELLT: total 7 with at least 6 in each component. Oxford Test of English Advanced: total 145 with at least 135 in each component. How old your English language tests can be Tests no more than two years oldThe following English language tests must be no more than two years old on the 1st of the month in which your programme starts, regardless of your nationality:IELTS AcademicTOEFL-iBT (including Home Edition)Trinity ISEOxford ELLTOxford Test of English AdvancedTests no more than three and a half years oldAll other English language tests must be no more than three and a half years old on the 1st of the month in which your programme starts, regardless of your nationality. Degrees taught and assessed in English We 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.UKVI list of majority English speaking countriesWe 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).Approved universities in non-MESCHow old your degree can beIf you are not a national of a majority English-speaking country, then your degree must be no more than five years old on the 1st of the month in which your programme starts.This time limit does not apply to your degree if you are a national of a majority English-speaking country. Find out more about our English language requirements Find out about other English language qualifications we accept, including professional qualifications.English language requirements Programme details Research profile Our research interests include:non-commutative ring theorynon-commutative algebraic geometryrepresentation theoryquantum algebracategory theoryalgebraic geometryhigher and derived categoriessymplectic geometryalgebraic and geometric topologyarithmetic geometry Our research community 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 100+ 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.Piscopia InitiativeWe particularly encourage women and those who identify as women plus other underrepresented groups in mathematics to apply, and to work with groups such as the Piscopia Initiative to improve the representation and inclusion of women and minorities in mathematics.Piscopia Initiative Find out more about pursuing a PhD in the School of Mathematics in this Q&A with the Director of the Graduate School. Programme structure This programme is delivered by the Algebra, Geometry and Quantum Physics (AGQ) Centre for Doctoral Training, which spans across 3 leading Scottish universities: the University of Glasgow, Heriot-Watt University and the University of Edinburgh.On this programme, you must take taught courses while completing the research elements of a traditional PhD programme.We have designed the programme to be flexible in how you can acquire credits. However, during the 4-year programme, you must successfully complete:180 credits of taught courses over the first 3 yearsthe equivalent of 3 years of PhD researchOver the first 3 years, you will complete 90 credits of taught courses, including:Year 1: 30 credits from mandatory cohort activities, including a group projectYear 2: 30 credits from advanced computing coursework and a computing projectYear 3: 30 credits from an internship or placementYou will accrue the remaining 90 credits during Years 1 and 2 by:taking up to 6 courses from a broad selection offered on topics across algebra, geometry, mathematical physics, and their interfacesand/orparticipating in approved reading groups or seminarsBrowse available courses on the AGQ website Support As part of a cohort-based training centre, you will receive extensive additional training beyond your thesis research, with emphasis on communication and leadership skills as well as research computing skills.You can also take part in student-led reading groups that focus on your areas of interest:Cohort reading groups Facilities You will be part of a world-class, interdisciplinary research community at the University of Edinburgh. Students from our partner institutions, Heriot-Watt University and the University of Glasgow, will also participate in the CDT cohort.You will have access to all three institutions' facilities, including:common meeting and study spaceparticipation in research seminars with a wide range of international visitorsYou will also be able to participate virtually in activities at the different institutions.CDT students at our University will have dedicated desk space:for Year 1, in the state-of-the-art Bayes Centre (where many cohort activities take place)for Years 2 to 4, in the James Clerk Maxwell Building Careers Career opportunities Graduates of this programme will be well-prepared to find employment and to become leaders in a diverse array of industries, including:academia and researchin the industrial sector, in areas such as:techfinanceconsultancycryptography and securityquantum technologiesin the third sector, in areas such as:public engagementgovernmentpolicyeducation Careers Service Our Careers Service can help you to fully develop your potential and achieve your future goals. The Careers Service supports you not only while you are studying at the University, but also for up to two years after you finish your studies. With the Careers Service, you can: access digital resources to help you understand your skills and strengthstry different types of experiences and reflect on how and what you developget help finding work, including part-time jobs, vacation work, internships and graduate jobsattend careers events and practice interviewsget information and advice to help you make informed decisions Visit the Careers Service website Life at Edinburgh Accommodation We guarantee an offer of University accommodation for all new, single postgraduate taught students from outside the UK and new, single postgraduate research (typically PhD) students who:apply for accommodation by 31 July in the year when you start your programmeaccept an unconditional firm offer to study at the University by 31 Julystudy at the University for the whole of the academic year starting in SeptemberUniversity accommodation websiteAccommodation guarantee criteriaWe also offer accommodation options for couples and families.Accommodation for couples and familiesIf you prefer to live elsewhere, we can offer you advice on finding accommodation in Edinburgh.Accommodation information from the Edinburgh University Students' Association Advice Place Societies and clubs Our societies and sports clubs will help you develop your interests, meet like-minded people, find a new hobby or simply socialise.SocietiesSport Clubs The city of Edinburgh Scotland's inspiring capital will form the background to your studies — a city with an irresistible blend of history, natural beauty and modern city life. Find out more about living in Edinburgh Exercise, leisure and support facilities Outside of your studies, we offer a range of facilities that you might find useful day-to-day, including:sport and exercise facilitiesUniversity cafes and cateringEdinburgh University Students' Association (EUSA) venues and shopsa multi-faith chaplaincy for all faiths and nonea University nursery (based at King’s Buildings campus) Health and wellbeing support You will have access to free health and wellbeing services throughout your time at university if you need them.The support services we offer include: a student counselling service a health centre (doctor's surgery) support if you're living in University accommodation dedicated help and support if you have a disability or need adjustmentsHealth and wellbeing support services Disability and Learning Support Contact General enquiries CDT Manager, Joyce Ternenge Email us Phone:+44 (0)131 650 5085
