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.
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