Simon Andrew Dobson, FRSE

Accepting Postgraduate Research Students

PhD projects

Network science emerged as a way of applying concepts from statistical physics to a wide range of systems that can be represented as pairwise interactions. It has been extremely successful as a framework for modelling phenomena ranging from crystal formation to epidemic spreading.

However, it is now clear that this approach has some severe limitations. Firstly, not all interactions are pairwise: many occur only when a larger group of components are brought together, for example in social interactions, animal flocks, robot swarms, or chemical reactions. Secondly, a process' evolution may be affected by the fine structure of the network, in terms of the exact details of how neighbourhoods are formed. Thirdly, both these phenomena may vary in time and space, so that the process' evolution itself evolves and self-organises alongside the evolution of the underlying network and its higher-order features.

All these phenomena have been studied individually, using network tools such as simplicial complexes or hypergraphs combined with analysis techniques based on (discrete) sheaves and differential geometry. We are however still seeking a thorough treatment, both mathematically (to model the interactions analytically) and computationally (to simulate these processes accurately, efficiently, and at scale). We therefore need to extend both the theory and practice of network science to encompass higher-order interactions with significant dynamic behaviour.

I'm looking for students wanting to contribute to the study of higher-order networks, using some appropriate mixture of theory and practice: both are equally important in addressing the scientific questions of interest. This would suit someone with an interest in complex systems, network science, and simulation (in some combination). Our experimental work is conducted almost exclusively using Python, and we have a considerable investment in computational tooling, including libraries for network processes and simplicial topology that can be used as starting points for experiments. We also have several potential application areas, including in epidemic modelling and sensor networks for environmental and ecological projects, in conjunction with other groups within St Andrews.