EPSRC Centre for Doctoral Training in Mathematical Analysis and its Applications:Maxwell Institute Graduate School in Analysis & Applications - MIGSAA

Lead Research Organisation: University of Edinburgh
Department Name: Sch of Mathematics


In this proposal we seek to establish a Centre for Doctoral Training in Mathematical Analysis and its Applications.

The main purpose of the centre is to train upwards of 60 new PhD students in this area over several years, and in doing so address the proven skills need for highly-trained researchers in this area.

The centre will be founded on rigorous mathematical analysis and its applications, with a strong focus on nonlinear partial differential equations, under three broad themes: theoretical, stochastic and numerical. Its scope includes harmonic analysis, mathematical analysis of large-scale discrete structures, applied analysis, dynamical systems, stochastic analysis, financial mathematics, applied probability and computational mathematics. There will be a special emphasis on the connections and interactions between these areas, and their applications, and active collaboration with industry -- in the formulation of student projects, in mentoring PhD students, in developing work placements for the students, and more broadly in two-way knowledge exchange -- will be a key feature of this CDT.

The need for mathematicians trained in this centre is manifest in real-world phenomena where cutting-edge differential and/or stochastic models are needed, for example in oil extraction, in power grid renewable energy strategies, in finance processes, in ecological impacts of climate change, and in procceses inside the brain.

We shall provide a flow of such PhDs with multiple skill sets and the ability to deal with the sophisticated challenges arising in mathematical modelling: they will be able to both analyse and implement and will be in a position to mount rapid and agile responses to current and future challenges.

MIGSAA training will be constructed on two main pillars: outstanding academic provision and early-stage career development.
These are underpinned by development of a strong sense of cohort. As a fully integrated joint 4 year PhD programme, it will offer much more than the standard UK Mathematics PhD model.

Initial academic training will build upon the firm foundation provided by SMSTC, and will feature a strong taught and assessed component.
Students will also complete two assessed projects during their first year. It is intended that the two projects will span the areas of MIGSAA, and will provide a firm basis for choosing the topic for the main PhD dissertation towards the end of Year 1. The main PhD project, which will be challenging and substantial, will lead to original research findings at the cutting edge of mathematical endeavour.

A tranche of specially designed, more advanced courses will be available for students in Year 2 and beyond so that students will continue to consolidate the available knowledge and expertise as they continue on their main research project. Students will be further supported by a carefully-planned programme of complementary research activities.

There will be a strong focus on early-stage career development in its broadest sense. This will include training in public engagement, effective collaboration, understanding the impact agenda and responsible innovation, leadership, outreach, media training, engagement with industry and networking.

Central to our vision for MIGSAA is the sense of cohort which it will foster. Beginning with the annual induction event, the cohort environment already offered by participation in SMSTC will be significantly enhanced by provision of contiguous office accommodation and dedicated common spaces, with Year 1 students collocated at ICMS in central Edinburgh. For the later years cohort activities include: physical attendance at higher level courses, research seminars and generic skills courses; active working groups encouraging peer-to-peer learning; annual residential symposia.

Planned Impact

This CDT will produce 60+ internationally competitive PhDs in the Priority Area Mathematical Analysis and its Applications who have the training required to address the acknowledged skills need for researchers at a high level in this area both in academia and in industry and commerce, and who are able to make major contributions to UK research and economic competitivity.

Particular areas of industrial and commercial relevance include modelling processes ranging from oil extraction, power grid renewable energy strategies and finance processes, ecological impacts of climate change, and the study of processes in the brain. Research carried out at MIGSAA has the potential to have an impact on the development of new technologies, improved health/medical care,
and on national planning/social policy.

An award of a CDT will unlock support from the universities and commercial and industrial sources in various forms and will fuel a virtuous circle in the development of the research undertaken and its exploitation. It will cement an already strong relationship that the Maxwell Institute has with industrial and commercial partners, with long-term benefits to all parties.

MIGSAA has already received expressions of support from industrial partners Selex and supporters Dstl and others, and ongoing collaboration is planned in the formulation of student projects, in mentoring PhD students, in developing work placements for the students, and more broadly in two-way knowledge exchange. We will run a quarterly series of invited industry-oriented talks and workshop sessions. The students will thus be introduced to a wide range of application areas and industries to which their skills could be applied, and will become keenly aware of the context and potential impact of their research.


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