An EPSRC Doctoral Training Centre in Geometry and Number Theory


London School of Geometry & Number Theory


Am I expected to be interested in both geometry and number theory? What if I already have definite interests and want to specialise?

With our broad base of supervisors, we can hopefully cater to your specialist interests as well as offering you the opportunity to spend some time in the first year learning a variety of other stuff. Having a basic grounding in the terminology and a familiarity with the canonical examples across a range of subjects will help you communicate with the other mathematicians in your cohort.

How is the London School of Geometry and Number Theory different from a standard PhD programme?

The biggest difference is in the structure of the first year: there will be more emphasis on broadening your knowledge base and on helping you to make an informed choice of supervisor for the following three years. Another difference is the flexibility of deciding (after one year) on a supervisor from any of the three institutions.

Will I have to teach?

There is no formal requirement to teach. However, opportunities to teach will be available on an ad hoc basis. Many of our existing graduate students find teaching interesting and rewarding. Doing some teaching while at the LSGNT can provide valuable experience which will be relevant when you look for your next job.

What does the first year involve?

The first year is not like the typical first year of a UK PhD. It is closer to the first year of graduate school in North America (but you will not have to do any teaching!). Go to course info for more details.

Is there assessment? Are there exams?

We shall monitor progress in the first year to ensure that what we offer is relevant and useful and in particular is a good preparation for your PhD research project. One of the first-year projects will be marked, and you will have to give a presentation on it. There will also be assessed presentations as part of the topics courses.

Where will I be based?

In the first year you will be based at UCL. The training will be structured so that you will spend days or half-days at King's and Imperial every week during term. This will help you to meet graduates and potential supervisors at all three institutions. For years 2–4 you will be enrolled as a PhD student at one of the three institutions. Your offer letter may give a sub-list containing two institutions. This means that you can expect to be registered at one of these from year 2. For students from overseas (non-EU) the institution from year 2 will be fixed as part of the offer of a place. Moreover any student funded via the Heilbronn Institute for Mathematical Research will be based at UCL.

How and when do I choose a supervisor?

We expect to recruit students with a wide variety of backgrounds: some of you will want a particular person as your first supervisor, others will want to spend some time exploring before making this important decision. If you have a clear idea about which supervisor you want, you should get in touch at the time you apply to the LSGNT and explore the possibilities. Bear in mind that in some cases a particular supervisor may not be able to commit to taking you on. In this case you would need to keep an open mind. There are many supervisors available with overlapping interests and it is likely that you can be co-supervised by your supervisor of choice, with a collaborator as your first supervisor. If you do not know who you would like as PhD supervisor, you will need to start thinking about the possibilities in the second term of your first year (January–March). You will have met many possible supervisors by then: you should try to discuss research projects with a few of them to get a feel for what is available. We shall also provide a list of supervisors and available projects and support you in making this important decision.

Am I eligible to apply?

You are eligible to apply if you hold (or will hold in September) a 4-year degree in mathematics or a closely related subject and satisfy the institutional English language requirements.

What is the funding situation?

We shall offer 14–15 fully funded 4-year studentships this year, including one Heilbronn studentship which is restricted to UK nationals. There is limited funding available for full funding (including non-EU fees) for non-EU students. There is ample funding for UK and EU students. These studentships cover both fees and pay a stipend at EPSRC's standard rate. The current rate is £17,432 per annum for 2020/2021, including a London allowance of £2,000 per annum. Income tax is not payable on this stipend. We expect that many students will contribute to their department's teaching: you will be paid on an ad hoc basis for any teaching undertaken. Each studentship comes with a generous allowance to help cover costs of hardware, travel and a placement either in an overseas maths department or in industry.

How do I go about finding accommodation?

You may find the following useful, though they are mainly aimed at undergraduates: