PhD & Postgraduate Research

The department offers the opportunity to study for a research degree in any of the areas of interest of our staff members.

We offer the following PhD programs in the department:

PhD in Mathematics
PhD in Statistics
PhD in Statistics (Integrated): a four-year PhD programme which involves successful completion of postgraduate level (MSc) courses and a dissertation during the first year before progressing onto the PhD
PhD in Applied Social Statistics: on subjects related to statistical approaches to social sciences problems

You can find details of our research areas on our research pages, and we welcome direct contact to discuss possible projects. Lancaster is also home to the Statistics and Operational Research Centre (STOR-i) and is a participant in the North West Social Science Doctoral Training Partnership.

Students have a formal weekly meeting with their supervisor, but we usually supplement this with more frequent, informal contact. We will cover any skills gaps through additional lecture programmes or directed reading. You will have the opportunity to attend graduate lectures on topics of current research interest. You will also be able to participate in national schemes such as APTS, MAGIC and NATCOR and take part in internal seminars for students and staff. These are an ideal opportunity to gain valuable experience of communicating ideas to an audience while also receiving feedback, which can help set future research directions.

All PhD students have a departmental laptop of their own and encourage you to attend and present work at national and international conferences. Each new PhD student is also assigned an individual peer mentor. Your mentor will be a current senior PhD student, who you can approach for guidance regarding university-related concerns that you may encounter during the first year.

How to Apply

The application process is explained step-by-step here. Please click the headings to move to the next topic.

How to apply
Find a supervisor
Apply online
What to include
When to apply

The first step if you are interested in studying for postgraduate research is to find and contact a suitable supervisor, making sure that they are willing to supervise you. We suggest mentioning the name of your prospective supervisor in your personal statement.

Application Process

Identify and contact the prospective supervisor.
Begin the online application process.
After an initial screening, we will invite UK based applicants to visit the department to meet your potential supervisor and other staff. (We provide support for standard travel costs.) For overseas-based applicants we will offer a Skype meeting.
Following steps 2 and 3, you might be offered a choice of possible PhD projects.
If you do not require financial support from the University, you will quickly be informed of our decision. Otherwise, your application will be considered on a competitive basis with others; you will be informed of the decision after the application deadline (31 January).
Completion of visa requirements for overseas candidates.
Arrive in Lancaster to start your PhD.

The most important considerations when choosing to study for a PhD or MPhil are the project and supervisor. For this reason, we invite all UK based applicants to discuss research projects with potential supervisors. Whilst we welcome proposals for research projects from applicants, most research projects are developed by academics taking into consideration applicants’ strengths and knowledge.

At the bottom of this page, you can see a sample of possible projects offered by our staff, but please note that this list is only indicative and is not exhaustive. You should contact members of staff directly for more details. You might also wish to look at our research pages, to learn more about our specialisms.

All applicants for postgraduate study in the Department of Mathematics and Statistics need to complete an online application via the University Postgraduate Admissions Portal.

Once you have created an account at our Postgraduate Admissions Portal you will be able to fill in your personal details, background and upload supporting documentation.

Current Lancaster Students

If you are a current Lancaster student, or you have recently graduated from Lancaster, we can reduce the amount of information that you will need to provide as part of your application. You will need to provide only one reference and will not need to supply your Lancaster degree transcript.

You will need

Postgraduate application form, available once you have created an account in the online portal and selected your mode of study.
Two references – you should include at least one academic referee who can comment on your academic quality, performance and potential to pursue independent research.
Transcripts of previous higher education degrees or other courses that you have completed or for which you are currently studying. Please note, for transcripts in languages other than English, a certified English translation will be required.
A detailed CV (up to 3 pages) – this should cover academic achievements, past projects and any employment history.
Personal statement (up to 2 pages) – you should include information on your research interests, relevant experiences and the subject area that you would like to work in, and if possible, the name of the supervisor(s) you would like to work with.
If English is not your first language, proof of English language competency is required.
- IELTS is the recommended test but we consider tests from other providers; please refer to the university's information on language requirements. If you have any concerns or questions, please contact the Faculty Postgraduate Admissions team for clarification.
- Our requirements for IELTS are an overall score of at least 6.5, with no individual element below 6.0. If your score is below our requirements but all individual elements are at least 5.5, we may consider you for one of our pre-sessional English language programmes.

Please note that the Department does not require applicants to submit a research proposal. This is optional, but if an applicant would like further guidance on this issue, please contact the relevant PhD admissions tutor with the subject line your intended programme (e.g. PhD Mathematics or PhD Statistics etc.).

Entry date: our academic year starts in October and most students enter at this time. Entry in January or April is also possible. Applications are considered throughout the year.
Timeline: Applications are normally considered between October and May of the following year.
Categories of candidates: Different studentships have different eligibility criteria but broadly cover 3 categories: UK students, UK/EU students and Overseas (non-EU) students. All eligible applicants are automatically considered for available studentships.
Studentships deadline: Due to high demand for studentships we have a deadline of 31st January. All applications received by this date will receive equal consideration. Applications received after this deadline will be considered for any remaining studentships.
Final studentships decisions are usually made by April but please feel free to contact us to find out whether studentships are still available.

There are additional special funding routes available in Statistics which have their own deadlines. Please visit the websites of the STOR-i Centre for Doctoral Training and North West Social Science Doctoral Training Partnership for more information.

Research Areas

Ranked joint 5th in the 2014 Research Excellence Framework (REF), Lancaster is one of the UK's top departments for research in mathematics and statistics.

Pure Mathematics

Statistics

STOR-i Centre for Doctoral Training

Current Funding Opportunities

Details of any currently advertised funded PhD studentships are given below. You are strongly encouraged to contact the prospective supervisor before making an application.

Note that the majority of funding opportunities for October entry in any given year close before March of that year.

Department PhD Studentships in Mathematics and Statistics in 2019/20

Overview

The Department of Mathematics and Statistics at Lancaster University is inviting applications for fully-funded PhD positions in either Pure Mathematics or Statistics for the entry in October 2020. Please see the PhD in Mathematics and PhD in Statistics course pages for details.

Research projects

Any research areas in Pure Mathematics or Statistics that are consistent with those of our staff members are considered and some examples of research topics and potential supervisors are available.

Entry Requirements

Applicants are expected to have a minimum of an upper-second class honours degree, or its equivalent, in Mathematics, Statistics or related fields. Preferably applicants will, or are expected to, hold a first class degree in MSci/MMath for Mathematics, MSc in Statistics/Data Science, though exceptional BSc students will also be considered.

Funding eligibility

The studentship normally covers full payment of tuition fees at UK/EU level plus a stipend for living expenses. All applicants from UK/EU/Overseas may apply. The funding is offered for 3.5 years of study for UK/EU candidates and 3 years of study for Overseas candidates.

Application process

The deadline for submitting applications for this studentship is 31 January 2020. The guidelines on the application process are found in the How to Apply section. Note that all eligible candidates from the standard PhD applications are automatically considered.

Contact

Those interested are encouraged to contact the PhD Admissions Officer, Dr J. Park (juhyun.park@lancaster.ac.uk). Please provide your CV and transcripts.
EPSRC PhD Studentships in Mathematical Sciences

Following substantial recent investment in the Mathematical Sciences at Lancaster University, we invite applications for up to 14 fully funded PhD studentships in Pure Mathematics, Statistics and Operational Research for entry in October 2020.

Full details may be found on our Studentships in Mathematical Sciences webpage.

Self-Funded Opportunities

The Department also considered applications from self-funded students. Please contact the PhD admissions tutor, Professor Andrey Lazarev, to discuss this possibility.

Studentships and Funding

As a postgraduate research student, you can be funded from several different sources:

Research Council Studentships: full payment of tuition fees plus a stipend for living expenses for UK applicants only. EU applicants may apply but normally only fees are paid.
EU-funded Studentships: normally full payment of tuition fees (at UK/EU level) plus a stipend for living expenses. No restrictions on applicants, unless specified, but overseas applicants would need to pay the difference in fees.
Department Studentships: normally full payment of tuition fees (at UK/EU level) plus a stipend for living expenses. No restrictions on applicants, unless specified, but overseas applicants would need to pay the difference in fees.
ESRC Studentship competition: The North West Social Science Doctoral Training Partnership (NWSSDTP) holds an annual competition for studentships, which can be used for study towards a PhD in Statistics or Social Statistics. The NWSSDTP is a collaboration between Lancaster, Manchester and Liverpool universities and offers an excellent range of PhD programme pathways and training courses for students who are part of this innovative scheme. Candidates may apply for funding towards masters and doctoral (1+3/2+2) study, or doctoral study only (+3/+2).
Normally the competition for October entry takes place in January or February in the year of entry and requires a PhD proposal with a nominated supervisor. If you are interested, you are expected to contact the department before with an idea for a PhD proposal and find a supervisor who can work with you towards making an application.
Studentships funded by industry and other external sources: normally full payment of tuition fees (at UK/EU level) plus a stipend for living expenses. No restrictions on applicants, unless specified but overseas applicants would need to pay the difference in fees.
Self-funding: student responsible for tuition fees and living expenses. No restrictions on applicants.

PhD Supervisors

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Professor Alexander Belton CMath, CSci, FIMA, SFHEA

Applications to join the department's thriving PhD programme are welcome from students with interests in analysis, probability theory or mathematical physics. The area in which I work, non-commutative probability, is an exciting combination of these three subjects. Knowledge of all of them is not necessary, but an interest to discover more is.

At present I'm particularly interested in the following topics.

Quantum random walks. A classical random walk consists of repeatedly flipping a coin and moving left or right accordingly. This simple model illustrates many important ideas in probability theory. Its quantum generalisation corresponds to a system interacting with a sequence of identical particles; limit theorems have been obtained, but many interesting questions remain unanswered.
Non-commutative stopping times. Stopping times are random times which, at any given moment, are known to have occurred or not. The time of the first rainfall this week is a stopping time; the time of the last rainfall is not. The theory of stopping times is vital for developing classical theories of stochastic integration. The proper non-commutative generalisation is known, but is yet to be exploited fully.
Exotic forms of independence. The concept which separates probability from analysis is stochastic independence. Once one moves to the non-commutative world, more than one form of independence exists. Free independence was introduced by Voiculescu in the 1980s, and has important connections to random matrix theory, quantum information theory and representation theory. Connections for other forms of independence remain to be explored.

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Professor Gordon Blower

I an interested in supervising PhDs in the following topics: Random matrices, high dimensional phenomena, and optimal transportation theory. Specifically, I would be willing to supervise a project `Integrating differential equations in random matrix theory'. This would involve using methods from the theory of linear systems to analyze various operators which arise in random matrix theory. In particular, the aim is to extend ideas of Tracy and Widom to new matrix models. To pursue this project, a student would need a sound background in analysis. While the results have applications to statistical physics, the student would not require much background in physics or probability. This project develops a theme from some previous PhD thesis which I have supervised at Lancaster. Further information is available on request.

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Dr Yemon Choi

Availability

I would be interested in taking new PhD students for a 2021-22 start. I am keen to hear from applicants with a strong background in functional analysis. Some previous exposure to representation theory of groups or the general theory of (matrix) Lie groups would be desirable.

Current ideas for PhD projects

Here are three possible areas in which I am willing to supervise: each of these is not a specific PhD project, but a setting in which there are various possible research problems that a student could work on. If you would like to know more, then please feel free to get in touch.

Algebras associated to group actions on L^p spaces
Cohomological invariants of Fourier algebras
Properties of Banach-Kähler modules

Warning notes.

Themes 1 and 2 are likely to require some prior exposure to the basic theory of C*-algebras. However, some of the necessary background can be learned in the initial stages of the PhD, and depending on the individual strengths of an applicant there may be particular projects that require less functional-analytic machinery; some questions may be suitable for those with solid basic analysis and interests in the representation theory of finite groups.

It is possible that you are reading this and have had some exposure to various structural properties of Banach algebras known as "approximate amenability", "character amenability", or "module amenability". I will not, for the foreseeable future, supervise on any of these three, nor on any hybrid of these.

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Professor Gabor Elek

Graph limits. Topological dynamics.

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Dr Daniel Elton

Interested in supervising doctoral students working on topics in the spectral theory of partial differential operators, particularly those arising in mathematical physics and/or with connections to other areas of mathematics. Potential projects could focus on zero modes of Pauli and Dirac operators, operators with periodic or quasi-periodic coefficients and the stability of embedded eigenvalues.

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Dr Jan Grabowski SFHEA

I am currently offering PhD projects in three areas: 1. Quantum groups, including producing novel quantum groups from the double bosonisation construction. 2. Cluster algebras, their quantizations and representation theory. 3. Relationships with mathematical physics, including Verlinde algebras, quantum cohomology and integrable systems and their relationships to quantum cluster algebras.

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Dr Robin Hillier

I offer PhD supervision in areas around the mathematics of conformal field theory, operator algebras, and quantum information theory.

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Professor Thomas Jaki

Using existing information in multi-arm multi-stage clinical trials

Multi-arm clinical trials compare several active treatments to a common control and have been proposed as an efficient means of making an informed decision about which of several treatments should be evaluated further in a confirmatory study. Additional efficiency is gained by incorporating interim analyses that allow the study to be stopped early - either because of overwhelming evidence of benefit or lack thereof.

This project will investigate design and analysis of multi-arm multi-stage clinical trials that incorporate existing information (e.g. from previous studies). A Bayesian framework will be use to integrate this information while frequentist properties of the design will be controlled.

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Dr Rebecca Killick

PhD proposals are welcome in the broad areas of time series analysis, nonstationarity, changepoints, wavelets, streaming data as well as environmental and medical applications.

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Professor Dmitry Korshunov

Tail asymptotics for perpetuities in continuous time; Heavy-tailed analysis of linear functionals of random walks and Levy processes

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Dr Niels Laustsen

I am happy to supervise PhD students who wish to work on a project related to my research expertise in Operator Theory and Non-commutative Analysis. Possible topics include: ideals of the algebra of bounded operators on a Banach space; the existence of approximate identities in such ideals; commutators and traces.

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Professor Andrey Lazarev

Homological algebra and derived categories
Higher structures and noncommutative geometry
Deformation theory of geometric and algebraic structures
Operads and Topological Field Theories
Rational homotopy theory

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Dr Mark MacDonald

I would be interested in taking a PhD student who has some familiarity with algebraic geometry and representation theory. A PhD student of mine would address open questions in the theory of linear algebraic groups over fields. I have potential PhD projects in mind related to birational invariant theory, and also to linear representation theory in positive characteristic.

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Professor Nadia Mazza SFHEA

I would be happy to supervise PhD students for a research project in modular representation theory of finite, infinite discrete and profinite groups and related topics (such as group cohomology), on Mackey functors and Burnside rings, or on (pro-)fusion systems and related topics.

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Dr Kanchan Mukherjee

I welcome new PhD students with strong background in statistics and probability to work on projects related to robust estimation in nonlinear time series models and resampling.

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Dr Christopher Nemeth

I would be happy to supervise a PhD student who is interested in computational methods for Bayesian inference. In particular, the development of new MCMC and SMC algorithms for big data and intractable likelihood problems.

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Dr Anthony Nixon

I would be interested in discussing PhD opportunities with a student interested in combinatorics, geometry or both. In combinatorics I am interested in graph theory, matroid theory and combinatorial rigidity. In geometry I am interested in discrete and computational geometry, sphere packing and concrete aspects of differential and algebraic geometry. Unifying these topics is the study of geometric graphs and their configuration spaces. As well as the above purely theoretical topics, I am interested in applications of these topics to biophysical materials and control of robotic formations.

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Professor Stephen Power

Geometric rigidity, infinite bond-node structures, crystallographic and quasicrystallographic bar-joint frameworks, rigidity operators, rigid unit modes, locally compact graphs and string-node meshes.

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Dr Bernd Schulze

Geometric and combinatorial rigidity. Discrete structures. Symmetry.

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Dr Chris Sherlock

Projects are available in combinations of (1) MCMC theory: efficiency as a function of tuning parameters, and convergence; (2) MCMC methodology: developing new algorithms or variations on existing algorithms; (3) MCMC applications in e.g. the environment or veterinary epidemiology; (4) particle filters and bridges for stochastic processes.
Example MCMC areas include: pseudo-marginal, delayed acceptance, HMC, non-reversible, and MCMC and variations for tall data.

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Dr Adam Sykulski

I am interested in supervising PhD students in the broad areas of time series and spatial statistics. Proposals are welcome in developing methodological and computational advances in space-time “big data” analysis, as well as the application of such methods in areas including oceanography, climate, public health, and finance.

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Dr Andrew Titman

I am happy to supervise students in topics related to medical statistics. I would particularly welcome applicants interested in developing methodology for the analysis of event history data using multi-state models.

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Dr Amanda Turner

My main research area is in probability with a specific focus on scaling limits of stochastic processes. My work combines ideas from probability theory, real and complex analysis and statistical physics, so I would be interested in discussing possible projects with students who have a strong background in any of these areas.

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Dr Jennifer Wadsworth

I am happy to supervise PhD topics in all aspects of extreme value theory. In particular multivariate and spatial extremes are exciting areas with lots of work to be done on relaxing assumptions so that models are more realistic.

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Dr Fang Wan

I am happy to supervise students in topics related to medical statistics. I would particularly welcome applicants interested in multiple comparison, simultaneous inference and adaptive design.

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Student and Alumni Stories

Graduating students and alumni can give you a real flavour of life at Lancaster and how we can change your life and launch your career.

Helen

“My PhD showed me how we can use mathematics and statistics in practice to make real life decisions”

Rhian

“The opportunity to tackle interesting, challenging problems encouraged me to go on to further study”

Jon Barry

Former Mayor of Lancaster Jon Barry completed a PhD in Statistics at Lancaster in 1996.

Eddie Bell

In his handmade raw-selvedge Oni 512 jeans, one might guess that Eddie Bell is a designer, but this data scientist works for an E-fashion company and has coined his own title of ‘fashematician’.