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MIGSAA Programme


The Maxwell Institute Graduate School in Analysis and its Applications (MIGSAA) is a Centre for Doctoral Training that provides high quality instruction in analysis and the applications of analysis to a wide range of areas. MIGSAA has been made possible by a grant from the UK's Engineering and Physical Sciences Research Council and the Scottish Funding Council.

A CDT where you can benefit wholeheartedly from the experience of academic staff at two great institutions. I can't think of any other place that would allow me to pursue two varying topics at two universities. - A current MIGSAA student

PhD study in MIGSAA may be undertaken with over 40 supervisors and on topics ranging from pure analysis to applied mathematics relevant for scientific, engineering, environmental or social challenges. Most projects will relate to one of the following themes:

  • Partial Differential Equations dispersive PDE and probabilistic methods, linear and nonlinear elliptic PDEs, transport, generalised spectral theory, analysis of PDEs arising in geometry, numerical methods.
  • Harmonic Analysis including the interaction with discrete structures, geometric topics, number theory, large data sets.
  • Stochastic Analysis Markov decision processes, stochastic differential equations and stochastic partial differential equations - including both theoretical and numerical analysis, stochastic filtering, limit theorems, stability and convergence rates, large deviations and rare events.
  • Interdisciplinary and Industrial Mathematical Modelling for environmental and ecological systems, atomic and molecular systems, climate extremes, social phenomena and energy networks, networks and biological applications.
  • Numerical Analysis in fluid dynamics, molecular and biological models, for stochastic and/or partial differential equations, finite element and spectral methods and multiscale numericalmethods.
  • Continuum Mechanics including complex fluids, turbulence, porous media, solid mechanics, wave propagation and scattering, granular media.
  • Pure and Applied Probability communication networks (wired, wireless, mobile), energy networks, biochemical networks, disease modelling, random graphs, percolation theory, and wavelet methods.

What’s the difference compared to a “standard” PhD programme?

In a standard PhD, students are admitted with a named supervisor in mind, who will direct the research that the student undertakes. This leads to the completion of the PhD thesis after around 3 – 3.5 years of study.  Such PhD students are experts in their chosen field, but there is increasing demand from both students and employers for greater breadth of study and more opportunity for engagement with industry and commerce.

In a CDT, students are admitted to the programme (rather than with a specific supervisor), and take PhD training courses and projects over their first year which help shape their perspective, leading to a match with a supervisor sometime in the second half of Year 1. It is still the case that the research project directed by the supervisor is the centrepiece of the PhD, but this is augmented by an on-going training programme in Years 2–4 of the student’s studies.  This provides a much broader experience, both academically and in connection with real-world applications. The statistics demonstrate that this breadth leads to greater employability, both in academia and elsewhere.

Note that the MIGSAA PhD is a 4-year programme and MIGSAA students are funded for the full 4 years.


The best part was definitely getting to know unfamiliar areas of maths. It was helpful to see how everything complements each other in making topics more understandable. - A current MIGSAA student

Our intention is that all MIGSAA students gain awareness of the full intellectual spectrum of research in analysis and its applications, including familiarity with theoretical issues, stochastic techniques, numerical methods and examples of how analysis problems impact the sciences and engineering. Therefore we expect all students to take some training spanning these areas – even though their eventual PhD thesis may specialise in only one or two.

In the modern world theoreticians need to know about implementation of their results and likewise applied mathematicians need an understanding of the underlying theory. And stochastics are (literally) to be found everywhere!


Expanding one’s horizons in mathematics is a lifelong endeavour. In the top North American and European institutions PhD students, postdocs and academic staff attend advanced courses on a regular basis. We will be offering a suite of advanced courses within MIGSAA (and beyond) and it is expected that MIGSAA students will continue to attend some of these into their second, third and fourth years.

Year 1

During Year 1 there is group project work in the autumn and spring, and a more substantial individual project from mid-March into the summer, possibly leading on to a thesis topic.

You will also follow a collection of courses during Year 1, mainly from the SMSTC, but some specially designed for MIGSAA students at Advanced Level. There will be a progression board to confirm progress to Year 2 and beyond – in much the same way as progression to Year 2 is currently handled at the two universities.

Sharing the experience

Being put together with a strong cohort of other students, particularly given their diverse backgrounds and interests, has meant that there are always people around to motivate, support, and assist mathematically, as well as making sure that there is no risk of becoming isolated with work. - A current MIGSAA student

It is well established that young researchers in mathematics thrive when they are well-connected to each other and not working in isolation. It is also recognised that learning with and from your peers is very important. For these reasons all our Y1 students share office space in 15 South College Street, where SMSTC courses take place. The experience of working together and taking the same suite of courses cannot be underestimated in this first developmental year.

We also hold a number of pan-MIGSAA events for Y2 – Y4 in order to encourage these connections to continue to grow: crash courses, mini-symposia, residential symposia, MIGSAA Student Colloquium, peer-learning topic-focused interactive research workshops...

You will also enjoy all the benefits of everything that is offered in the Graduate Schools of Mathematics at UoE and HWU.

MIGSAA Student Case Studies   View all Case Studies here 

EPSRC Centres for Doctoral Training transforming research  EPSRC CDT brochure (p8)