Topological spaces occur almost everywhere in mathematics. It has been particularly fruitful to study homotopies of these spaces (and maps between them). Symmetries appear everywhere in mathematics, so it is logical to study topological spaces that have symmetries. In turn we should look at homotopies that preserve these symmetries. This area is known as equivariant homotopy theory.
Equivariant homotopy theory is particularly exciting when one considers groups of symmetries that have their own topology. To make the theory tractable, one usually assumes that the groups are compact. There are two large classes of compact groups that have been useful: the compact Lie groups, such as O(n) or U(n), and the profinite groups, like the p-adic integers.
Recent work of the adviser and a PhD student [BS20a], [BS20b], has constructed a link between (stable) equivariant homotopy and the theory of sheaves with a group action in the case where G is a profinite group. Many questions on this topic remain, particularly those connected to monoidal structures (a form of categorical multiplication, inspired by the Cartesian product of topological spaces), change of groups functors and to what extents these results can be applied to compact groups in general.
The student should have attended courses on algebraic topology and topology. Some algebra will also be useful. This project will require the student to become familiar with the abstract language of model categories [DS95] and modern categories of spectra [MM02] and [MMSS01].
[BS20a] D. Barnes and D. Sugrue. The equivalence between rational G-sheaves and rational G-mackey functors for profinite G. Preprint, available as arXiv:2002.11745, 2020.
[BS20b] D. Barnes and D. Sugrue. Equivariant sheaves for profinite groups. Preprint, available as arXiv:2012.03982, 2020.
[DS95] W. G. Dwyer and J. Spali´nski. Homotopy theories and model categories. In Handbook of algebraic topology, pages 73–126. North-Holland, Amsterdam,1995.
[MM02] M. A. Mandell and J. P. May. Equivariant orthogonal spectra and Smodules. Mem. Amer. Math. Soc., 159(755):x+108, 2002.
[MMSS01] M. A. Mandell, J. P. May, S. Schwede, and B. Shipley. Model categories of diagram spectra. Proc. London Math. Soc. (3), 82(2):441–512, 2001.
The Mathematical Research Centre conducts world-class research in the following areas: Algebra, Analysis, Operator Algebras, Algebraic Topology, Topological Data Analysis, PDEs, Survival Analysis, Bayesian Networks, Data Analytics and Operational Research. It maintains vibrant international links with a large number of researchers around the globe and regularly hosts international conferences and research visitors.
Mathematics at Queen's is joint 1st for Research Intensity in the UK. Mathematics is also joint 6th in the UK for Graduate prospects.
List of researchers, their interests and upcoming PhD projects can be found at:
Mode of study / duration
Registration is on a full-time or part-time basis, under the direction of a supervisory team appointed by the University. You will be expected to submit your thesis at the end of three years of full-time registration for PhD, or two years for MPhil (or part-time equivalent).
- The School has many industry links, some of which are with Seagate Technology R&D, Andor Technology and AVX Ltd. Many of our graduates take up positions with these companies in posts such as Statistical Analysis Programmer, Trainee Accountant, Financial Engineer and Business Analyst.
- Queen’s is ranked in the top 140 in the world for graduate prospects (QS Graduate Employability Rankings 2020) with Mathematics at Queen's being joint 6th in the UK. Graduates from the School take up employment through a number of companies such as Allstate, AquaQ Analytics, Citigroup, Deloitte, PwC, Randox, Seagate and UCAS.
World Class Facilities
- Since 2014, the School has invested over £12 million in new world-class student and staff facilities. Maths and Physics students now have their own teaching centre that opened in 2016 housing experimental physics laboratories, two large computer rooms for mathematical simulations and student study plus a student interaction area.
In addition, Northern Ireland has the lowest student cost of living in the UK (Which? University, 2018) being £5000 per year cheaper for students to live in Northern Ireland compared to London (Which? University 2018).
- Students will have access to our facilities, resources and our dedicated staff. The School of Mathematics and Physics is one of the largest Schools in the University. Staff are involved in cutting-edge research that spans a multitude of fields.
Information on the research interests and activities of academics in the Mathematical Science Research Centre can be found at https://web.am.qub.ac.uk/wp/msrc/. These interests fit into the themes: Algebra, Analysis, Data Science, Optimization and Operational Research, Partial Differential Equations, Statistics, Topology and Geometry.
Mathematical and statistical skills are in great demand in the economy, particularly the advanced skills developed at the PhD level.
Employment after the Course
As well as continuing in research careers, our PhD graduates have also gone on to work in finance, computing, data analysis, management and teaching. Our advisors will be happy to provide further information on the career prospects arising from your chosen research area. Further information on careers can be obtained from the School and the Faculty.
People teaching you
Dr David Barnes
Head of Centre - Mathematical Sciences Research Centre
Dr Ying-Fen Lin
Postgraduate Advisor - Mathematical Sciences Research Centre
Assessment processes for the Research Degree differ from taught degrees. Students will be expected to present drafts of their work at regular intervals to their supervisor who will provide written and oral feedback; a formal assessment process takes place annually.
This Annual Progress Review requires students to present their work in writing and orally to a panel of academics from within the School. Successful completion of this process will allow students to register for the next academic year.
The final assessment of the doctoral degree is both oral and written. Students will submit their thesis to an internal and external examining team who will review the written thesis before inviting the student to orally defend their work at a Viva Voce.
Supervisors will offer feedback on draft work at regular intervals throughout the period of registration on the degree.
Students will enjoy the benefits of modern practical laboratories, extensive computer facilities and interactive spaces.
The minimum academic requirement for admission to a research degree programme is normally an Upper Second Class Honours degree from a UK or ROI HE provider, or an equivalent qualification acceptable to the University. Further information can be obtained by contacting the School.
For information on international qualification equivalents, please check the specific information for your country.
English Language Requirements
Evidence of an IELTS* score of 6.0, with not less than 5.5 in any component, or an equivalent qualification acceptable to the University is required. *Taken within the last 2 years.
International students wishing to apply to Queen's University Belfast (and for whom English is not their first language), must be able to demonstrate their proficiency in English in order to benefit fully from their course of study or research. Non-EEA nationals must also satisfy UK Visas and Immigration (UKVI) immigration requirements for English language for visa purposes.
For more information on English Language requirements for EEA and non-EEA nationals see: www.qub.ac.uk/EnglishLanguageReqs.
If you need to improve your English language skills before you enter this degree programme, INTO Queen's University Belfast offers a range of English language courses. These intensive and flexible courses are designed to improve your English ability for admission to this degree.
|Northern Ireland (NI) 1||£4,596|
|Republic of Ireland (ROI) 2||£4,596|
|England, Scotland or Wales (GB) 1||£4,596|
|EU Other 3||£18,000|
1 EU citizens in the EU Settlement Scheme, with settled or pre-settled status, are expected to be charged the NI or GB tuition fee based on where they are ordinarily resident, however this is provisional and subject to the publication of the Northern Ireland Assembly Student Fees Regulations. Students who are ROI nationals resident in GB are expected to be charged the GB fee, however this is provisional and subject to the publication of the Northern Ireland Assembly student fees Regulations.
2 It is expected that EU students who are ROI nationals resident in ROI will be eligible for NI tuition fees, in line with the Common Travel Agreement arrangements. The tuition fee set out above is provisional and subject to the publication of the Northern Ireland Assembly student fees Regulations.
3 EU Other students (excludes Republic of Ireland nationals living in GB, NI or ROI) are charged tuition fees in line with international fees.
All tuition fees quoted are for the academic year 2021-22, and relate to a single year of study unless stated otherwise. Tuition fees will be subject to an annual inflationary increase, unless explicitly stated otherwise.
There are no specific additional course costs associated with this programme.
Additional course costs
Depending on the programme of study, there may also be other extra costs which are not covered by tuition fees, which students will need to consider when planning their studies . Students can borrow books and access online learning resources from any Queen's library. If students wish to purchase recommended texts, rather than borrow them from the University Library, prices per text can range from £30 to £100. Students should also budget between £30 to £100 per year for photocopying, memory sticks and printing charges. Students may wish to consider purchasing an electronic device; costs will vary depending on the specification of the model chosen. There are also additional charges for graduation ceremonies, and library fines. In undertaking a research project students may incur costs associated with transport and/or materials, and there will also be additional costs for printing and binding the thesis. There may also be individually tailored research project expenses and students should consult directly with the School for further information.
Some research programmes incur an additional annual charge on top of the tuition fees, often referred to as a bench fee. Bench fees are charged when a programme (or a specific project) incurs extra costs such as those involved with specialist laboratory or field work. If you are required to pay bench fees they will be detailed on your offer letter. If you have any questions about Bench Fees these should be raised with your School at the application stage. Please note that, if you are being funded you will need to ensure your sponsor is aware of and has agreed to fund these additional costs before accepting your place.
How do I fund my study?1.PhD Opportunities
Find PhD opportunities and funded studentships by subject area.2.Funded Doctoral Training Programmes
We offer numerous opportunities for funded doctoral study in a world-class research environment. Our centres and partnerships, aim to seek out and nurture outstanding postgraduate research students, and provide targeted training and skills development.3.PhD loans
The Government offers doctoral loans of up to £26,445 for PhDs and equivalent postgraduate research programmes for English- or Welsh-resident UK and EU students.4.International Scholarships
Information on Postgraduate Research scholarships for international students.
Funding and Scholarships
The Funding & Scholarship Finder helps prospective and current students find funding to help cover costs towards a whole range of study related expenses.
How to Apply
Find a supervisor
If you're interested in a particular project, we suggest you contact the relevant academic before you apply, to introduce yourself and ask questions.
To find a potential supervisor aligned with your area of interest, or if you are unsure of who to contact, look through the staff profiles linked here.
You might be asked to provide a short outline of your proposal to help us identify potential supervisors.