UCL Graduate degrees


London School of Geometry and Number Theory MPhil/PhD

The London School of Geometry and Number Theory (LSGNT) is an EPSRC-funded Centre for Doctoral Training (CDT) and is a joint venture between UCL, King's College London and Imperial College London. It offers a wide range of research projects in different aspects of number theory, geometry and topology.

Key information

Programme starts

September 2021

Modes and duration

Full time: 4 years

This is four-year full-time, fully-funded PhD programme taught across UCL, King's College London and Imperial College London.

Application dates

All applicants
Open: 9 November 2020
Close: 31 December 2020

Tuition fees (2021/22)

£5,525 (FT)
£22,740 (FT)

Note on fees: The tuition fees shown are for the year indicated above. Fees for subsequent years may increase or otherwise vary. Further information on fee status, fee increases and the fee schedule can be viewed on the UCL Students website: ucl.ac.uk/students/fees.

Location: London, Bloomsbury

Entry requirements

Applicants are expected to have completed at least a very good four-year degree in mathematics or a closely related discipline by September 2020; in Europe this implies a Master’s degree for most applicants. We also welcome applications from outstanding US bachelor students, for example. Please note we do not expect you to have completed your four-year degree before you apply for our programme, but you must expect to complete this before your entry to our programme in September.

English language requirements

If your education has not been conducted in the English language, you will be expected to demonstrate evidence of an adequate level of English proficiency.

The English language level for this programme is: Standard

Pre-Master's and Pre-sessional English

UCL Pre-Master's and Pre-sessional English courses are for international students who are aiming to study for a postgraduate degree at UCL. The courses will develop your academic English and academic skills required to succeed at postgraduate level. International Preparation Courses

Further information can be found on our English language requirements page.

International students

Country-specific information, including details of when UCL representatives are visiting your part of the world, can be obtained from the International Students website.

International applicants can find out the equivalent qualification for their country by selecting from the list below.

Select your country:


Mathematics research at UCL is flourishing with significant funding from EPSRC, ERC, the Royal Society and industry. The department is a member of the UCL Institute of Origins, Centre for Inverse Problems, and CoMPLEX (Centre of Mathematics and Physics in the Life Sciences and Experimental Biology); it hosts the Clinical Operational Research Unit and has 20 postdoctoral researchers including the Clifford Fellow. The London School of Geometry and Number Theory is run by UCL in partnership with King's College London and Imperial College London. Students benefit from our leading role in the inter-university London Taught Course Centre for PhD Students in the Mathematical Sciences.

Research areas

  • Geometry and Number Theory
  • Pure Mathematics
More information can be found on the department website: London School of Geometry and Number Theory MPhil/PhD

About this degree

In the first year a broad mathematical training is offered across the three participating institutions. The emphasis is on topics in geometry and number theory and will consist of topics modules and interface lectures, a computer programming course, seminars, lectures from both the London Taught Course Centre (LTCC) and the Taught Course Centre and two mathematical mini projects of between 15,000 and 50,000 words each.

Towards the end of their first year, Home/EU students will choose a project and supervisor from one of the two institutions indicated on their original offer, and enrol at the college of their primary supervisor where they will complete their mathematical research thesis of 100,000 words. Overseas students will have already been assigned to a supervisor/institution during their recruitment and will move to that institution at the start of year two.  All LSGNT CDT students will continue to have access to, and attend events at, all three institutions (UCL, King's and Imperial) during the entirety of their PhD programme.

In the third or fourth year, students will have the opportunity to spend up to three months either on an industrial placement or in a mathematics department outside London. The Heilbronn studentship gives the student the opportunity to spend two months per year during their PhD working at the Heilbronn Institute for Mathematical Research.

Please note that the list of modules given here is indicative. This information is published a long time in advance of enrolment and module content and availability is subject to change.

Additional costs

For more information on additional costs for prospective students please go to our estimated cost of essential expenditure at Accommodation and living costs.


Details of the accessibility of UCL buildings can be obtained from AccessAble accessable.co.uk. Further information can also be obtained from the UCL Student Support & Wellbeing team.


Our LSGNT studentships are all fully funded, including fees, a stipend and a grant to cover travel expenses to attend conferences/workshops. For 2018/19 we have funding for 14-15 studentships, funded by the EPSRC, UCL, Imperial College London and King's College London.

Scholarships relevant to this department are displayed below.

CSC-UCL Joint Research Scholarship

Fees, maintenance and travel (Duration of programme)
Based on academic merit

UCL Research Opportunity Scholarship

UK rate fees, a maintenance stipend, conference costs and professional development package (3 years)
Based on both academic merit and financial need

For a comprehensive list of the funding opportunities available at UCL, including funding relevant to your nationality, please visit the Scholarships and Funding website.


The first intake of students to the CDT was in 2014. Recent UCL Mathematics graduates have taken up academic posts at universities such as UCL, Sheffield, Kyoto and California State; others have joined the financial services industry at companies such as Barclays Capital, Schroders, Deloitte, ABN Amro and J P Morgan; and others have become mathematics teachers and computer programmers. Some students have taken summer secondments, with two recent ones at the Department of Business, Innovation and Skills.


Many students go on to careers in financial services in the City, and in innovation and technology. Many others proceed to postdoctoral research and academic careers. The LSGNT CDT has several industrial partners including Satellite Applications Catapult, Schlumberger, Heilbronn Institute for Mathematical Research, the Bank of England, Morgan Stanley and G-Research.


Students interact closely with their peers from all three institutions within the CDT (UCL, Imperial and King’s) and those universities within London via the LTCC, as well as other UK universities including Bath, Cambridge and Oxford. Students attend seminars both within and outside the departments of all three institutions and are exposed to a vigorous conference programme. Students also interact with the CDT’s industrial partners, the Bank of England, Morgan Stanley, Schlumberger, Satellite Applications Catapult and G-Research.

Why study this degree at UCL?

The training that we offer will differ from a traditional UK PhD in pure mathematics in a number of respects, and particularly in the first-year mathematical training that will take place across the three institutions.

The LSGNT has an ethos of working and learning together in a friendly and supportive environment. The collaborative spirit established in the first year will be maintained by a number of mechanisms including cross-college supervision teams, junior seminars, working groups, and other activities such as a new LSGNT colloquium, and intensive workshops.

Department: Mathematics

What our students and staff say

Staff review

"In a joint venture, UCL recently received EPSRC funding for a Doctoral Training Centre, called the London School of Geometry and Number Theory, and I am involved in several aspects of this programme. London is the perfect place for a number theorist: we have a regular joint number theory seminar with King's and Imperial (and sometimes with Paris!), there is funding for visitors, and we get many applications from excellent PhD students. I also love teaching at UCL, as we get many students who are very bright, enthusiastic and fun to work with. "

Professor Sarah Zerbes

London School of Geometry and Number Theory MPhil/PhD
Student review

"[I chose UCL] because the LSGNT programme includes a first year consisting of courses and projects, during which you can choose your supervisor and re..."

Emily Maw

London School of Geometry and Number Theory PhD

Application and next steps


Students are advised to apply as early as possible due to competition for places. Those applying for scholarship funding (particularly overseas applicants) should take note of application deadlines.

This programme requires two references. Further information regarding references can be found in our How to apply section.

Application deadlines

All applicants
31 December 2020

For more information see our Applications page.

Apply now

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Page last modified on 28 August 2021