Professor Stephen Coombes,
Deputy Head of School,
Professor of Applied Mathematics
I enjoy collaborating with my colleagues in mathematical sciences, mainly on the mathematics relevant to my interests in neuroscience, but also on topics further afield in the broader area of pattern forming systems in physics and biology. The environment here is ideal for multi-disciplinary work and it is a privilege to collaborate with colleagues from outside the school, and in particular from biology, psychology and the Queens Medical Centre.
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"Initially it was an interest in astronomy that drew me to a career in academia and then I realised that a professional career in this area needed a healthy dose of advanced training.
My relationship with mathematics was secured when I studied as an undergraduate at The University of Exeter, Theoretical Physics. I then moved to Kings College, London and studied for my PhD researching a topic on neurocomputing.
My academic career began at Loughborough University in the Department of Mathematical Sciences where I was a senior lecturer. I then joined The University of Nottingham and have spent twelve years in the School of Mathematical Sciences. My current role is Deputy Head of School, Professor of Applied Mathematics and member of the mathematical biology research group.
I’ve always worked in an academic environment, apart from a one-year break after my first degree when I worked as a math's tutor.
Why I love mathematics
I think the thing I most enjoy about mathematics is seeing models of the world simplified and realised before you as symbols on a piece of paper. I enjoy collaborating with my colleagues in the mathematical sciences, mainly on the mathematics relevant to my interests in neuroscience, but also on topics further afield in the broader area of pattern forming systems in physics and biology. The environment here is ideal for multi-disciplinary work and it is a privilege to collaborate with colleagues from outside the school, and in particular from biology, psychology and the Queens Medical Centre.
I am working in mathematical neuroscience with a particular interest in the use of nonlinear dynamics to understand aspects of the human central nervous system. I am actively championing this new field of mathematics at the national and international level, coordinating a UK network on Mathematical Neuroscience co-creating the new Journal of Mathematical Neuroscience and directing a Marie Curie Initial Training Network on Neural Engineering.
I am currently interested in developing mathematical models for the generation of brain signals seen in neuroimaging studies. As well as working with colleagues from the Sir Peter Mansfield Magnetic Resonance Centre I am also working with the following Nottingham labs: Neuronal Networks Electrophysiology Laboratory, Institute of Hearing Research, Academic Radiology, Visual Neuroscience. The aim in all cases is to develop mathematical theory that can be applied to problems in neuroscience. This ranges from understanding the dynamics of neurons in a dish, through models of neural networks for sensory processing right up to developing learning rules to achieve natural computation.
I am very proud to be the director of NETT, which is a European PhD training programme helping deliver a new breed of scientists capable of developing transformative technologies based upon ideas from neuroscience. It is exciting to see the use of mathematics for developing and understanding complex neural engineered systems of a sort that will have an impact on almost every aspect of future human life, including the development of neural prosthetics, next generation computing via synthetic cognition, and brain-machine interfaces.
Over the next few years I also intend to work on a major advancement in the subject of neural fields. To date they have had a major impact in understanding a variety of neural phenomena, including EEG rhythms, visual hallucinations, and anaesthesia. Yet, as currently formulated, they lack important physiological mechanisms known to be fundamental in generating brain rhythms, including dendritic structure and cortical folding. I will develop models with a stronger connection to biological reality and hand-in-hand the set of new mathematical tools required for their understanding. This work will pave the way to a deeper understanding of brain dynamics and neural computation.
In particular it will provide a fundamental underpinning for understanding neuroimaging signals, develop a new framework for feature-based computation such as for motion perception, deliver new biologically motivated systems for solving spatial navigation tasks, and generally advocate for the ability of brain-inspired non-von Neumann architectures to solve real world problems.
Importantly I will develop a sound theoretical bedrock for this work using, and developing, powerful modern tools from the mathematical sciences, including those from differential geometry, uncertainty quantification, scientific computation, nonlinear dynamics and stochastic optimal control.
I run – slowly."