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.

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:

Details of our research areas may be found on our research pages and staff welcome direct contact to discuss possible projects. Lancaster is also home to the STOR-i Statistics and Operational Research Centre for Doctoral Training, and is a participant in the North West Social Science Doctoral Training Partnership.

Students have a formal weekly meeting with their supervisor, but in most cases this is supplemented by more frequent, informal contact. Any skills gaps will be covered through additional lecture programmes or directed reading, and students have the opportunity to attend graduate lectures on topics of current research interest, national schemes such as APTS, MAGIC and NATCOR which provide PhD level courses, 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 their own departmental laptop, and are generously supported 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.

The first step if you are interested in studying for postgraduate research is to contact the relevant PhD admissions tutor (Mathematics - Prof Andrey Lazarev; Statistics - Dr Juhyun Park), letting us know which areas of mathematics or statistics you might be interested in researching. We will put you in touch with potential supervisors, help you to efficiently navigate the applications systems and the funding opportunities.

Application Process

  1. Contact the appropriate PhD admissions tutor for an initial discussion.
  2. Begin the online application process.
  3. After an initial screening, we will invite UK based applicants to visit the department to meet potential supervisors. (We provide support for standard travel costs.) For overseas based applicants we will offer a Skype meeting.
  4. Following steps 2 and 3, you might be offered possible PhD projects/supervisors to choose from.
  5. 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).
  6. Completion of visa requirements for overseas candidates.
  7. 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 competencyis 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 any applicant would like further guidance on this issue, please contact the relevant PhD admissions tutor with 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.

Join our Graduate Training Programme at Lancaster University

Research training

We take care of all of our students at Lancaster University. The Faculty of Science and Technology runs a series of training sessions designed to improve your skills and abilities during your PhD.

Learn more

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).
    The competition for October 2018 entry is now closed.  If you are interested in October 2019 entry, you need to contact the department by the end of December 2018 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.

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.  

  • PhD project linked to the EPSRC grant "Scalable Data Science for Security and Location-based Data", partially sponsored by a project partner, the Heilbronn Institute for Mathematical Research (HIMR).

    Supervisors: Dr Chris NemethDr Simon Lunagomez-Coria and Dr Vasileios Giotsas
    Start Date: October 2019 (flexible)

    Incredible technological advances in data collection and storage have created a world in which we are constantly generating data. Analysing such large data sets creates significant statistical challenges, where it is necessary to trade between the speed and accuracy with which large volumes of data can be analysed and acted upon. Increasingly, recorded data exhibit a natural network structure, for example, friendship groups through social media. To extract key features from these data sets, it is important to account for the dependency in the network structure, however, including this dependence in our statistical models makes it more computationally challenging to analyse these data. The aim of this project is to develop statistically scalable inference tools for analysing large-scale network data, where the data may be temporally-evolving and what is learnt from the evolving network, and the associated uncertainty can aid in statistical learning procedures for identifying potential changes in network structure.

    To stimulate this methodological development, the student will collaborate with Dr Giotsas on the problem of network traffic hijacking. Traffic hijacking attacks exploit the fact that the Internet's core routing protocol lacks built-in security mechanisms, allowing any adversary with access on the routing system to inject fraudulent routes and execute an array of attacks, including DDoS, impersonation and eavesdropping [1]. We are now witnessing an alarming number of such traffic hijacking incidents that result in comprised critical infrastructure and services. The significant difficulty of preventing such attacks has attracted the attention of mainstream media [2], which illustrates the potential impact of this project.

    The successful candidate will be required to spend up to two months each summer working at HIMR gaining relevant experience. To be considered for this studentship, candidates must be UK nationals and prepared to undergo security clearance procedures.

    The studentship will be funded for a period of 4 years and covers the costs of university fees and will provide an annual tax-free stipend to the student (currently £16,776 per annum) plus increases for inflation.

    Applicants are expected to have a masters level degree in a mathematical discipline containing a significant amount of statistics. The ideal candidate would be familiar with advanced statistical methods and possess strong computer programming skills.

    Applicants interested in this position are encouraged to contact Dr Chris Nemeth ( for informal enquires. To apply for the studentship, candidates should complete an online application naming Dr Chris Nemeth as the supervisor.

    [1] Mitseva, Asya, Andriy Panchenko and Thomas Engel. "The state of affairs in BGP security: A survey of attacks and defences." Computer Communications (2018).
    [2] Sherman, Justin. "It's far too easy for countries like Russia and China to hijack Internet traffic." Slate Magazine, Slate, 16 Nov 2018.

Self-Funded Opportunities

The Department also considered applications from self-funded students.   Please contact the relevant PhD admissions tutor (Mathematics - Prof Andrey Lazarev; Statistics - Dr Juhyun Park) to discuss this possibility.

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.

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PhD Supervisors

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.

  1. 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.
  2. 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.
  3. 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.

View Alexander's profile

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.

View Gordon's profile


I am interested in hearing from suitable applicants wishing to start in 2019-20 or later.

Current ideas for PhD projects

Here are four possible areas in which I would currently be 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. I hope to add more details, or links to more details, in the near future: if you would like to know more then please feel free to get in touch.

  1. Algebras of convolution operators on Lp spaces
  2. Cohomological invariants for Fourier algebras
  3. Homological algebra for dual Banach algebras and their modules
  4. Classification problems for l1-semigroup algebras

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.

("Connes-amenability", on the other hand, is related closely to Theme 3 above, but be warned that this is an area with some nasty traps for the novice, primarily because dual Banach algebras are in some sense still not really understood.)

View Yemon's profile

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.

View Daniel's profile

Students who are interested on any of these topics are more than welcome to contact me for further details.

View Konstantinos's profile

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.

View Jan's profile

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

View Robin's profile

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.

View Thomas's profile

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

View Rebecca's profile

I am interested in supervising projects in geometric and combinatorial rigidity (both theory and application areas). I am particularly interested in rigidity properties of periodic structures, rigidity under alternative metrics, and aspects which border analysis, operator theory and Banach space geometry. A good background in either combinatorics or analysis is sufficient to get started. For more information please contact me.

View Derek's profile

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

View Dmitry's profile

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

View Andrey's profile

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.

View Mark's profile

modular representation theory of finite, infinite discrete and profinite groups; (pro-)finite groups; subgroup lattices of finite groups; group cohomology; Burnside rings; (pro-)fusion systems and related topics.

View Nadia's profile

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.

View Kanchan's profile

The understanding and control of infectious diseases is of considerable importance to society. How a disease spreads and/or how infectious a disease is, has tremendous implications upon the health and wealth of a community. I am interested in both the probabilistic and statistical analysis of infectious diseases. From a probabilistic perspective, we look to answer questions as: What is the probability that a disease takes hold within a community? How many individuals are ultimately infected by the disease? This involves developing novel probabilistic techniques to answer these questions for realistic population models such as the household and random graph models. Alternatively, having observed an epidemic we can propose a model for the disease spread and estimate the model parameters. However, often the disease data are "incomplete" and novel statistical methods, in particular, Markov Chain Monte Carlo (MCMC) are required to analyse the data. We aim to answer questions concerning the adequacy of the model and the predictive capabilities of the model for the future epidemic outbreaks.

View Peter's profile

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.

View Christopher's profile

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.

View Anthony's profile

Mendelian randomization, instrumental variables, meta-analysis, structural equation models.

View Tom's profile

1. Stochastic modelling and object oriented data analysis: This project develops a novel statistical methodology to analyse tree-like data (brain artery trees) based on a topological data representation. Standard methods try to extract high dimensional features from the representation for further analysis. This project considers a stochastic modelling approach similar to queueing models for statistical inference.

2. Prediction models for continuous monitoring data: It is easy to continuously collect and monitor various signals such as physiological or health related information, but is challenging to build a statistical model that takes such information into account. One can view such data as high-dimensional time series but there is more structural information/constraint that can be exploited. This project focuses on developing novel statistical methods using the ideas from functional data analysis and sparsity estimation.

3. Multivariate functional data analysis: Multivariate analysis is well developed for vector-like data, but not well developed for curve-like data such as continuous signals or functional data. Especially capturing (non-linear) dependence in high dimensional setting is challenging due to the inherent geometry of the data. This project develops novel statistical methods that combine the analytical (functional data analysis) and geometrical (shape analysis) approaches to analysing such type of data.

4. Spatial functional data and network regularisation: The spatial data has a natural network structure that is linked to each other through neighbours. When the dimension is high and the information is incomplete, it is difficult to estimate the underlying structure. This project considers to incorporate network regularisation methods in the context of spatial data analysis to tackle statistical inference problems.

View Juhyun's profile

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

View Stephen's profile

Geometric and combinatorial rigidity. Discrete structures. Symmetry.

View Bernd's profile

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.

View Andrew's profile

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.

View Amanda's profile

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.

View Jennifer's profile

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.

View Fang's profile