Study modes: Full-time, Part-time
Programme website: Analysis
Our analysis research group is one of the UK’s top centres for research in the field, especially in linear and nonlinear PDEs and harmonic analysis.
Your passion for mathematical analysis will be rewarded by contact with, and supervision by, world-leading academic staff, a rich seminar and working group programme and ultimately a qualification that boasts an internationally respected pedigree.
The School of Mathematics is a vibrant community of more than 60 academic and related staff supervising 60 students.
We have a unique focus on the interplay of classical Euclidean harmonic analysis with the modern theory of PDEs. We study harmonic analytic ideas in number theory, geometric measure theory, combinatorics, and discrete geometry and geometrically invariant inequalities; and we investigate applications of harmonic analysis to elliptic and parabolic PDEs with rough coefficients and/or on rough domains.
We also study:
- nonlinear hyperbolic, dispersive and kinetic equations and systems arising in the classical field theories of mathematical physics, mathematical biology and, in connection with black holes, mathematical general relativity
- free-boundary problems, optimal mass transportation and Monge-Ampère equations in nonlinear elasticity and other continuum theories
- well-posedness for supercritical initial value problems with noisy initial data
Mathematics is a discipline of high intellect with connections stretching across all the scientific disciplines and beyond, and in Edinburgh you can be certain of thriving in a rich academic setting. Our School is one of the country’s largest mathematics research communities in its own right, but you will also benefit from Edinburgh’s high-level collaborations, both regional and international.
Research students will have a primary and secondary supervisor and the opportunity to network with a large and varied peer group. You will be carrying out your research in the company of eminent figures and be exposed to a steady stream of distinguished researchers from all over the world.
Our status as one of the most prestigious schools in the UK for mathematics attracts highly respected staff. Many of our 60 current academics are leaders in their fields and have been recognised with international awards.
Researchers are encouraged to travel and participate in conferences and seminars. You’ll also be in the right place in Edinburgh to meet distinguished researchers from all over the world who are attracted to conferences held at the School and the various collaborative centres based here. You’ll find opportunities for networking that could have far-reaching effects on your career in mathematics.
In addition to the School’s excellent facilities, as part of the Analysis group you will have access to the activities of the Mathematical Analysis & its Applications (MIGSAA). Through seminars, mini-symposia and training courses, these stimulate and support development of research in analysis and theoretical nonlinear PDEs.
You will enjoy excellent facilities, ranging from one of the world’s major supercomputing hubs (EPCC) to generous library provision for research at the leading level, including the new Noreen and Kenneth Murray Library at King’s Buildings.
The School provides all postgraduates with access to software packages such as Maple, Matlab and Mathematica. We offer training in all the relevant programs you need to achieve your research aims.
As a research student, you will have your own desk with desktop computer and are allocated parallel computing time on 'Eddie', the Edinburgh Compute and Data Facility.
It is also possible to arrange use of the BlueGene/Q supercomputer facility if your research requires it.
These entry requirements are for the 2022/23 academic year and requirements for future academic years may differ. Entry requirements for the 2023/24 academic year will be published on 3 October 2022.
A UK first class honours degree, or its international equivalent, in an appropriate subject; or a UK 2:1 honours degree plus a UK masters degree, or their international equivalents; or relevant qualifications and experience.
Check whether your international qualifications meet our general entry requirements:
English language requirements
You must demonstrate a level of English language competency at a level that will enable you to succeed in your studies, regardless of your nationality or country of residence.
English language tests
We accept the following English language qualifications at the grades specified*:
- IELTS Academic: total 6.5 with at least 6.0 in each component.
- TOEFL-iBT (including Home Edition): total 92 with at least 20 in each component. We do not accept TOEFL MyBest Score to meet our English language requirements.
- C1 Advanced (CAE) / C2 Proficiency (CPE): total 176 with at least 169 in each component.
- Trinity ISE: ISE II with distinctions in all four components.
- PTE Academic: total 62 with at least 59 in each component.
Your English language qualification must be no more than three and a half years old from the start date of the programme you are applying to study, unless you are using IELTS, TOEFL, Trinity ISE or PTE, in which case it must be no more than two years old.
(*Revised 17 November 2021 to add accepted PTE Academic qualifications.)
Degrees taught and assessed in English
We also accept an undergraduate or postgraduate degree that has been taught and assessed in English in a majority English speaking country, as defined by UK Visas and Immigration:
We also accept a degree that has been taught and assessed in English from a university on our list of approved universities in non-majority English speaking countries.
If you are not a national of a majority English speaking country, then your degree must be no more than three and a half years old at the beginning of your programme of study.
Find out more about our language requirements:
Academic Technology Approval Scheme
If you are not an EU, EEA or Swiss national, you may need an Academic Technology Approval Scheme clearance certificate in order to study this programme.
- School of Mathematics funding opportunities
- Research scholarships for international students
- Principal's Career Development PhD Scholarships
UK government postgraduate loans
If you live in the UK, you may be able to apply for a postgraduate loan from one of the UK's governments.
The type and amount of financial support you are eligible for will depend on:
- your programme
- the duration of your studies
- your residency status.
Programmes studied on a part-time intermittent basis are not eligible.
Other funding opportunities
Search for scholarships and funding opportunities:
Select your programme and preferred start date to begin your application.
PhD Analysis - 3 Years (Full-time)
PhD Analysis - 6 Years (Part-time)
We encourage you to apply at least one month prior to entry so that we have enough time to process your application. If you are also applying for funding or will require a visa then we strongly recommend you apply as early as possible.