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Pure Mathematics Research MPhil/PhD

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We have a wide range of research opportunities in the three groups that make up the Pure section of the Department of Mathematics, namely the Analysis, Geometry and Number Theory groups. We recommend that you identify a broad research area that you are interested in and explore the webpage of the relevant research group(s). It might be the case that your interest spans more than one group.

 You will find links to the personal pages of each of the academic staff in each group and you should try to identify a potential supervisor, who you can then contact directly to discuss further.

You can explore potential supervisors on our research group pages below.  Click here for all the details on how to make an application.

Key information

Duration Full-time: 3-4 years; Part-time: 6-8 years.

Study mode Full-time, Part-time

Further details

Awarding institution King's College London/King's and HKU for joint programme

Faculty Faculty of Natural, Mathematical & Engineering Sciences

Department Department of Mathematics



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Course detail


Our department has a large number of active and internationally renowned researchers and postdoctoral research fellows. The research groups organise regular seminars, where top-ranking scientists from around the world present new results, which our research students can witness first hand. The students also organise their own informal seminars and discussion groups. The lively environment and the exceptionally friendly atmosphere at our department contribute to the high success rate of our students. You can apply for supervision in all fields of interest of our staff members. The department provides funding for PhD students to attend suitable schools and conferences during their studies.


More than 80% of the PhD students at the department are fully funded through a number of funding schemes; the most common is departmental funding which covers tuition as well as a living stipend. In recent years, on average, 10 students per year have been admitted to a PhD programme with funding from the department. 

Course study environment

You will be assigned a supervisor with whom you will work closely. You will also attend research seminars and take part in other research related activities in your research group, the department and more widely in the University of London. We do not specify fixed attendance hours, but we expect a good level of attendance, and our research students benefit from informal interaction with each other. You will be provided with access to working and storage space, as well as a laptop. On arrival you will discuss your research programme with your supervisor, and you will attend general induction sessions.

Postgraduate training

Carrying out research is learned in apprenticeship mode as PhD student works with a supervisor. Our PhD students receive various forms of training during their period of research, eg attending courses in the London Taught Courses Centre, attendance at EPSRC summer schools; provision of advanced lecture courses; College training courses for graduates who will give tutorial teaching to undergraduates; weekly seminars in the area of your research; frequent research group meetings; attendance at national and international conferences and research meetings. 

Communication skills are developed by preparing and presenting seminars in the department, assisted by your supervisor; apprenticeship in writing papers and, in due course, the PhD thesis.

To build your teaching skills and experience, you are strongly encouraged to apply to become a Graduate Teaching Assistant, giving tutorials to our undergraduates (training is provided)

Head of group/division

Head of Department: Professor Steven Gilmour

Contact for information

Contact the Admissions Office:

• Before you apply: via our Enquiry Form 

• To apply: here

• After applying: use the messaging service at King's Apply, Admissions Office Tel: +44 (0)20 7848 1648

Course website

Course website

Entry requirements

Entry requirements

Pure Mathematics Research entry requirements
Minimum UK requirements   The official minimum entry requirements are a Bachelor’s degree with 2:1 honours (or equivalent). In practice, applicants will normally be expected to have an MSc, MMath, MSci or equivalent degree with merit/2:1 honours (or equivalent) and high grades in modules relevant to the research area. Applications from women, disabled and minority candidates are encouraged, as are applications from individuals with non-standard backgrounds (e.g., those from industry or returning from a career break). It is not necessary that an applicant has completed their current course of study before applying; in such a case any offer may be conditional on the eventual degree classification.
  • Joint PhD: Humboldt University, Hong Kong University
  Find out more about applying for a joint PhD with the Humboldt University or Hong Kong University.  Students applying for the joint PhD programme with Humboldt University may be required to hold a Master’s degree in order to meet the requirements of Humboldt University.
International requirements   Visit our admissions webpages to view our International entry requirements.
English Language requirements  
  • Band D 
Visit our admissions webpages to view our English language entry requirements.


Application procedure

You can apply for supervision in all fields of interest of our staff members. Your application is considered and processed by the relevant admissions officers. We aim to reply within six weeks. To suitably qualified applicants, we offer opportunities to meet with prospective supervisors. Each November we hold an open day which provides information about our research activities and an opportunity to meet with relevant members of the department.

View our list of PhD projects to identify whether there is already a project proposed by a prospective supervisor in the area of research you are interested in. These projects indicate broad areas of potential research and there may still be a suitable supervisor available for your proposed area of research even if there are not any relevant projects here.

October, February, and June start dates are available. Applicants are strongly encouraged to start their degree at the beginning of the academic year in October, when the College offers a full induction programme.

Although there can be variations the selection process typically runs as follows:

Starting in February students are selected for interview. The interviews are held in March and a first round of offers is made. If an offer is declined then the groups make second round offers until the positions are filled. Research groups tend to fill their funded PhD positions first as these are the most competitive. Unfunded positions are rare as most supervisors will have taken on a funded student.

If you have any further questions please contact the Admissions Tutors or the Postgraduate Admissions Team.

You can also read our step-by-step guide on how to apply. 

Joint PhDs - Application advice

Applicants for the Joint PhD programme must contact the relevant departments at both universities before applying in order to discuss the suitability of their topic for the joint programme and to locate potential supervisors.

Applications should initially be submitted to the proposed home institution only, i.e., where the student will start and finish their programme. Students should note that acceptance onto the programme may take slightly longer than for single-institution PhDs because of the additional steps involved.  Further details, including guidance for applicants can be found on the King’s PhD funding pages.

Applicants who choose King’s as their home institution should apply through the online system, selecting the appropriate Joint PhD option from the drop-down list. In addition to the standard supporting documentation, applicants should submit a Travel Plan form indicating how they intend to divide their time between the two partner institutions. Students must spend a specified amount of time in each institution, details of which can be found in the ‘Notes’ section of the Travel plan form.

It is recommended that students submit applications for the Joint PhD programme by the end of March to begin the following September.

ATAS  An ATAS certificate is required for successful applicants applying for this course whose nationality is outside the European Economic Area (EEA) and Switzerland. For further guidance on obtaining an ATAS certificate can be found on our International Student Advice pages.

Personal statement and supporting information

You will be asked to submit the following documents in order for your application to be considered:

Document checklist
Research Proposal Yes

If you have identified a potential supervisor, you should discuss a research proposal with them. If you have not, or if you are potentially interested in several supervisors, you are not expected to write a detailed proposal. Instead, you should write a few short lines which clearly specify your research interests.

 For further advice on how to write a winning application, please visit this page.

Previous Academic Study Yes A copy (or copies) of your official academic transcript(s), showing the subjects studied and marks obtained. If you have already completed your degree, copies of your official degree certificate will also be required. Applicants with academic documents issued in a language other than English, will need to submit both the original and official translation of their documents.
References Yes Two references are required; professional references will be accepted if you have completed your qualifications over five years ago.
Other Optional You may also wish to include a CV (Resume) or evidence of professional registration as part of your application. 

Course intake

PhD: 8-20 FT, 2-5 PT per year; MPhil: 5-10 FT, 1-5 PT per year.

Application closing date

We recommend that you submit your application as soon as possible as we may need to request further information from you to assess your application. This is also important if your application is successful and you are required to meet any offer condition, and/or you need a Student Visa to study here at King's.

The final application deadlines are detailed below; on these dates, the programme will close at 23:59 (UK time) and we will open for the corresponding intake in 2023 soon after the same intake has passed in 2022.

  • June 2022 entry – 1 April 2022 for Overseas fee status and 11 April 2022 for Home fee status
  • October 2022 entry – 29 July 2022 for Overseas fee status and 26 August 2022 for Home fee status
  • February 2023 entry – 21 October 2022 for Overseas fee status and 22 November 2022 for Home fee status
  • June 2023 entry – 3 April 2023 for Overseas fee status and 17 April 2023 for Home fee status

Please note that funding deadlines may be earlier than the application deadlines listed above.

It is recommended that students submit applications for the Joint PhD programme with The University of Hong Kong or Humboldt University by the end of March to begin the following September.

Help and support

If you don't have a suitable qualification for direct entry to a UK university, or if English isn't your first language, our academic preparation courses can help you get ready for study in the UK.

International Foundation

Fees and funding

Mathematics Research

UK Tuition 2022/23

Full time tuition fees:

£6,120 per year (MPhil/PhD, Mathematics Research)

Part Time Tuition fees:

£3,060 per year (MPhil/PhD, Mathematics Research)

International Tuition Fees 2022/23

Full time tuition fees:

£22,980 per year (MPhil/PhD, Mathematics Research)

Part Time Tuition fees:

£11,490 per year (MPhil/PhD, Mathematics Research)

Mathematics Research with University of Hong Kong or Humboldt-Universität Zu Berlin

International Tuition Fees 2022/23

Full time tuition fees: 

£22,980 per year (MPhil/PhD, Mathematics Research with University of Hong Kong)

£22,980 per year (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)

Part time tuition fees: £11,490 (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)

All of these fees may be subject to additional increases in subsequent years of study, in line with King's terms and conditions.

Bench fees will be applicable to the non-award research programme for visiting students.

Financial help and support

Visit the fees and funding webpages to find out more about bursaries, scholarships, grants, tuition fees, living expenses, student loans and other financial help available at King's.

Career prospects

We have a dedicated team at King's Career & Employability centre who provide bespoke careers support for King's postgraduate researchers.


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Next steps

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