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Department of Mathematics
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London School of Economics
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London WC2A 2AE, UK


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PhD and MPhil in Mathematics

General Information for Prospective Research Students

The Department of Mathematics at the LSE is renowned for its research excellence within its areas of specialisation, which includes subjects in Mathematics that are applicable to the Social Sciences.Our research staff work in four broad disciplines - find out more about faculty in each area: Discrete Mathematics and AlgorithmsFinancial Mathematics and Control Theory, Game Theory, and Operations Research. Research is carried out over a wide range of specific areas, reflecting the diverse interests of our staff.  A complete list of all our researchers and their research interests can be accessed through our research page.

The Department of Mathematics was submitted jointly to REF 2014 with LSE's Department of Statistics: 84% of the research outputs of the two departments were classed as either "world-leading" or "internationally excellent" in terms of originality,
significance and rigour. The most recent work produced by members of the Department can be found on our publications page.

You can learn about the Department in the various sections of this website, including information about current and previous PhD students, and what some of our PhD graduates are doing now.

Applications for entry in 2018/19 are now open.


Opportunities for Research and Programme Structure

Supervision for MPhil/PhD research is available in combinatorics, combinatorial optimisation, computational learning theory, control theory, financial mathematics, game theory, graph theory, integer programming, mechanism design, polyhedral combinatorics, probabilistic analysis, theory of computation and algorithms, and in the applications of mathematics in areas such as inspections, network optimisation, telecommunications, transportation, and economics.

New students will initially be registered for the MPhil, and will be able to upgrade to PhD registration during their second year, depending on satisfactory progress (the MPhil has a maximum registration period of two years full-time). We do not consider applicants for the MPhil programme separately from the MPhil/PhD programme.

Taught Courses

In their first full year, all PhD students in the Department will attend four appropriate taught courses provided by either the London Taught Course Centre for PhD students in the Mathematical Sciences, or the London Graduate School in Mathematical Finance, depending on the focus of their research. Students may be asked to attend one or more courses from our MSc Applicable Mathematics, MSc Financial Mathematics or MSc Operations Research & Analytics degree programmes. In addition, students may substitute one or more of their taught courses for an LSE graduate course run by an associated department, with the approval of their supervisor(s).

Training, Seminars and Support

Training in established research techniques and development of a capacity in the student for original research in their chosen field of specialisation is provided through regular one-to-one meetings with the supervisor, as well as through directed reading. The final aim is to produce a thesis and subsequent publications that contribute to the development and understanding of the chosen area of mathematics. Please read our Programme Regulations for more information.

An important element of the training is participation in the various seminars organised by the Department (namely the Seminar on Combinatorics, Games, and Optimisation, the Joint Risk & Stochastics and Financial Mathematics Seminar and the co-hosted London Mathematical Finance Seminar). In addition, there are a number of seminars which are organised largely by and for research students on mathematical subjects, which they are required to contribute to at regular intervals:

Over the course of the year, the Department organises a number of personal development workshops for PhD students, designed to provide tailored support for specific areas of interest, such as careers, impact, final year processes, etc.

All research students in the Department are provided with some funding each year to encourage and support their research activities, such as conference attendance and purchasing books and technology. Additional research funds are also available, upon application.


Students will have access to the comprehensive facilities of the LSE Library and to the libraries of other colleges of the University of London. They will also benefit from the IT and other facilities available at the School.

Students are provided with their own workspace (at busy periods, hot-desking may be necessary) and Windows PC within the Department of Mathematics’ PhD study room.  This area was recently renovated, and has been modernised to become a professional, purposeful, and relaxed work environment. Students are thus offered a supportive environment within a community of scholars and are well-placed to pursue a career building on their research accomplishments. 

In addition to the space provided in Columbia House, a dedicated Postgraduate Common Room is available to students in 32 Lincoln's Inn Fields.  Students will also find the PhD Academy useful, a dedicated space and services hub for doctoral candidates.

How to Apply

The Department of Mathematics welcomes applications to study for MPhil/PhD degrees. Enquiries about research study in the Department can be emailed to PhD@maths.lse.ac.uk, or addressed to Professor Bernhard von Stengel, Department of Mathematics, LSE, Houghton Street, London WC2A 2AE. However, before doing so, please read the information below, which also contains some useful links to additional information.

A formal application is submitted through Graduate Admissions, but prior to this, you should submit an informal application to the Department of Mathematics. More information about informal applications can be found below. 

Key Details

Application Code: G1ZM

Duration: 3–4 years, full-time

Course details: here

Note that we do not normally offer MPhil/PhDs on a part-time basis, and that progression from MPhil to PhD usually takes place between years 1 and 2.

Entry Requirements

The criteria for the offer of a place include:

  • Your academic qualifications: a UK taught master's degree (MSc) with merit/distinction in a relevant area of mathematics or a non-UK equivalent in a relevant area of mathematics. Specific guidance for international graduate students can be found here.
  • Your English language ability must meet the LSE’s minimum requirements for graduate students studying research programmes.
  • The ability of the Department to provide adequate and appropriate supervision, with particular reference to your research proposal. We do not expect you to provide extensive research proposals as part of your application. Your research proposal is useful, however, in giving a flavour of your direction, ambition, and interests.
  • An interview for all short-listed applicants (via telephone, Skype or in person), unless there are exceptional circumstances preventing this.

Application Notes

  • We do not normally offer MPhil/PhDs on a part-time basis; usually, only full-time applicants can be considered.
  • We do not consider applicants for the MPhil programme separately from the MPhil/PhD programme.
  • Applicants are not required to submit GRE or GMAT scores when applying for this degree programme.
  • Formal applications are handled by Graduate Admissions, so any queries relating to your application and its progress should be addressed directly to them. Further general information about the School and its graduate programmes can be found in the Graduate Prospectus and corresponding web pages.

Informal Applications: Financial Mathematics

Before submitting a formal application to Graduate Admissions, prospective students should send an informal application email to the Research Manager to enquire about the possibility of making a formal application. It is essential that you include:

  • Full academic transcripts covering all study to date.
  • An up to date CV.
  • A brief research proposal with (1) a clear indication of the specific questions and direction of your proposed study within Financial Mathematics, (2) a short summary of your motivation to undertake a PhD, detailing what areas of mathematics you find especially engaging and important. An extensive literature review is not required.

The Research Manager will forward all informal applications to the Financial Mathematics PhD admissions team for consideration. Thereafter, the Research Manager will communicate the admissions team’s decision. If a formal application is advised, this should be made to Graduate Admissions following the normal application procedure outlined above.  If a formal application is not encouraged, unfortunately we cannot offer feedback on our decisions.

Do not contact potential supervisors directly, unless instructed to do so by the Research Manager.

Informal Applications: All Other Areas of Mathematics

Before submitting a formal application to Graduate Admissions, we advise prospective students to first find out more about potential supervisors by looking at the list of staff and their interests, which can be found through our research page. You should then email an informal application to members of the Department whose research interests most closely resemble your own to discuss possible research projects, preferably in detail. It is essential that you include:

  • Academic transcripts covering all study to date.
  • An up-to-date CV.
  • A brief research proposal with (1) a clear indication of the specific questions and direction of your proposed study, and (2) a short summary of your motivation to undertake a PhD, detailing what areas of mathematics you find especially engaging and important. An extensive literature review is not required. 

When contacting academic members of staff you should list which other members of the Department you have contacted or intend to contact, and copy in the Research Manager.

Once an appropriate research topic and supervisor have been identified, prospective students will be encouraged to submit a formal application through Graduate Admissions, following the instructions above.


Supervisors are selected during the application process. Students are assigned to:

  1. A principal supervisor with requisite knowledge in the student's chosen field
  2. An appropriate second supervisor.  Where appropriate, a second or joint supervisor may be appointed from another department, institute or programme.


Details of fees can be found here.

Financial Support

Financial support for MPhil/PhD study may be available from the School - for more information all on awards and scholarships, consult the Financial Support Office. All applications should be sent directly to the Department of Mathematics.

There is intense competition for all forms of financial support and MPhil/PhD applicants are urged to begin exploring all possible sources of funding internationally and in their own countries, as early as possible.

LSE PhD Studentship Scheme

The LSE offers a PhD Studentship scheme with full scholarships available to outstanding new PhD students. The scholarships cover fees and living expenses of £18,000 each year for four years. They are available for Home UK/EU and Overseas students undertaking full-time research in any LSE discipline, with annual renewal subject to satisfactory academic performance at the School. Studentships will be awarded on academic merit and research potential.

The Department of Mathematics can nominate a limited number of candidates for the studentships to each of the two funding board rounds available:

  • 8 January 2018
  • 26 April 2018

Award decisions will be made by a panel representing different academic disciplines at the School. The awards will be made solely on academic merit and research potential. This relates not only to an applicant’s past academic record, but also to an assessment of their chosen topic and to their likely aptitude to complete a PhD in the time allocated.

The studentships include a requirement that scholars contribute to their academic department as part of their research training, in the form of providing teaching or other work.

There is no separate application form for these awards. Selection will be based on the PhD application to the School. There will be three rounds of studentship selection, with a deadline attached to each round.  If you wish to be considered for an award, you must submit a complete application for a place on a PhD programme (including all supporting documentation such as references and transcripts) by the specified deadline.

FranklName: Nóra Frankl
Degree: currently holds an MSc in Mathematics from Loránd Eötvös University, Budapest; currently studying for a PhD in Mathematics (G1ZM)
Written in June 2017

What are you currently researching?
I am mostly interested in discrete geometry, which includes combinatorial questions about geometric objects. Sometimes I also think about purely combinatorial questions, for example I am currently working on a question about partitioning edge coloured hypergraphs into monochromatic cycles.

Why did you choose this area of study?
I like combinatorics and geometry, and this area is a mixture of these two.

What do you hope to do career-wise, long term?
I would like to stay in academia and do research.

Can you provide any advice to prospective students about the most effective way to approach research and keep stress levels down?
Of course, this varies from individual to individual and from area to area, but there are some things that can be useful in general. Set realistic expectations: you should not anticipate finding results quickly. It is a slow procedure. For me the recipe is to try to be happy even with small results: don’t let failure disappoint you too greatly. I think it is also good to not separate weekdays and weekends too much; when you have ideas and feel motivated, don't stop for the weekend, but treat yourself to much-needed rest days later.

What resources are available at LSE to help young researchers? 
There are several funds at both School and Departmental level.  Mathematicians need whiteboards – we’re lucky to have many in our PhD office, plus all the basic provisions we could ever need (stationery, printing, equipment, etc.).  Our PhD Office itself is a really good, productive environment to work in, where we can focus solidly on our research but also collaborate and share thoughts. The Department as a whole, alongside the PhD Academy and our Research Manager, assist with the essential practicalities of PhD study.  The Department invites key visitors to present at our seminar series. Crucially, we have a fantastic coffee machine in the Department :-)

In a few words, what is the best thing about studying at LSE?
Everyone is very nice; I am a valued member of the Department.

Ewan DaviesEwan Davies is a student of the MPhil/PhD in Mathematics who joined the Department in October 2013 under the supervision of Jozef Skokan and Peter Allen.  His research interests lie in combinatorics, particularly extremal graph theory and probabilistic combinatorics, as well as the intersection of these areas with other fields such as statistical physics and number theory.  During his time at LSE, amongst many other activities, Ewan has contributed extensively to the department, through committees and teaching, been awarded grants to facilitate his research visits and given many talks around the world.

Written in September 2016

I started my PhD at LSE after spending four years in Cambridge for a combined undergraduate and masters in mathematics. I wanted to retain the freedom and intellectual rigour of university life, but also move to a different city and discover new and exciting aspects of life outside work. A mathematics PhD in London was ideal for this; pure mathematics is a rigorous and highly distilled form of problem solving that I find exceptionally rewarding, and London is a near-limitless trove of opportunities to explore.

My work isn’t tied to a specific title or single unifying idea, I have enjoyed working on a variety of projects which are broadly from the same branch of mathematics, but use different techniques and ideas. This is great for motivation, there’s often something appealing to work on and I’m not pressured to make everything fit some central theme. Recently I’ve been focusing on a new method for optimising the observable properties of certain probability distributions that link combinatorics and statistical physics. With a few simple mathematical tricks I have been answering a variety of questions in combinatorics using ideas from statistical mechanics. I’m essentially analysing the average behaviour of a physical system with the property that any possible state of the system occurs with a probability proportional to its energy. Selecting an interesting system and the right definition of energy yields a variety of mathematical applications and I hope to spend the final year of my PhD trying to develop a general theory based on the early successful examples of the technique.

The atmosphere in the department at LSE is excellent; people are friendly, supportive and approachable. When I joined I was jokingly told, “we might not be the best maths department in the world, but we probably are the friendliest”. This succinctly captures the slightly British sense of humour and light-hearted environment that I’ve enjoyed being a part of. It’s also rather too modest, I frequently work with world-leading academics and feel very positive about the quality of the research I’m able to do here. After my PhD I hope to continue in academia with postdoctoral research, and I feel the high quality of the mathematics department at LSE is extremely beneficial for my goals. 

RobertsBarnaby Roberts is a student of the MPhil/PhD in Mathematics who joined the Department in October 2013 under the supervision of Peter Allen and Jozef Skokan.  His research interests lie in discrete mathematics, particularly Graph Theory. In his fourth, final year, Barnaby wrote this commentary about his time at LSE.

Written in March 2017



I’m a PhD student at LSE coming towards the end of my studies in Graph Theory.  Whilst I enjoyed undergraduate maths I didn’t want to dedicate so much time to maths without doing some of my own research.  Once I decided to pursue a PhD in Graph Theory I decided I wanted to go to a university where there were more than one academic in that area.  LSE was one of just a few such institutions in the UK.  In fact, LSE has a large and very active group of researchers in Graph Theory, Combinatorics and Discrete Mathematics.

I have loved research which, as well as being a good intellectual challenge, is also a surprisingly sociable activity.  Discussing ideas with fellow PhD students and other academics is a really invigorating experience and the atmosphere at LSE makes collaborations really easy to get involved in.  At LSE, my supervisors have been very flexible in allowing me to choose my own projects whilst also offering guidance and suggesting fruitful directions of study.  I have not only worked with other members of LSE but also with various people I have met at conferences and with invited guests who have visited LSE to give a seminars (we have a very active, engaging seminar series in Combinatorics, Games and Optimisation).

There are many aspects to a PhD beyond research.  Presenting work, attending conferences and teaching are all part of it too.  All three of those seemed a little daunting at first but quickly became really enjoyable.  Learning to present work well and similarly to teach maths clearly are both good challenges.  They are also very transferrable skills.  From being at LSE I have attended conferences across the world.  A particular highlight was spending 6 weeks in Brazil working with mathematicians in Rio and Sao Paulo.  This was made possible by funding accessible through LSE.

The Department of Mathematics’ PhD Prize for Outstanding Academic Performance

The Department of Mathematics’ PhD Prize for Outstanding Academic Performance was created in 2017, to be considered annually by a panel for the best PhD performance from a student completing in the previous academic year.

Awards will be made once per academic year, in the following December, with a view to presenting the award during the winter graduation festivities.

Bodies of work suitable for submission will normally be theses but, to allow flexibility in the nature of noteworthy work our students undertake, other original and promising contributions to research in Mathematics will be permissible.

A prize will not necessarily be awarded every year, and occasionally more than one award may be made.