Fraser graduated from the University of Cambridge in 2019 with an MMath degree. In his undergraduate studies he focused on applied mathematical methods and modelling, with particular interests in dynamical systems, perturbation methods, and mathematical biology. Before his final year at Cambridge, he spent the summer collaborating on a project examining how ethical issues can arise from the practice of mathematics, in conjunction with the Cambridge University Ethics in Mathematics project. During his Master’s year, he wrote an essay on finite compartment disease models and the (now somewhat infamous) basic reproductive ratio ‘R_0’. In his spare time, he enjoys reading science- and fantasy-fiction, learning languages, and practising archery.

Research project title:
Stochastic Pattern Formation

Supervisor(s):
Kit Yates, Jonathan Dawes

Project description:
First proposed as an explanatory model for morphogenesis, the paradigm of a ‘Turing pattern’ has been used to analyse the spontaneous emergence of coherent spatio-temporal structures in reaction-diffusion systems across a wide range of applications, from mathematical biology to nonlinear optics. In continuous deterministic models, this instability mechanism is well understood, and typical analysis can predict the leading order spatial characteristics and growth rates of these emerging patterns, as well as the parameter regimes in which they may be observed. Stochastic models have been shown to exhibit such patterns far outside the parameter regimes predicted by their deterministic counterparts. Fraser is exploring the analysis of these ‘Turing pattern’-like instabilities in lattice-based stochastic jump process reaction-diffusion models, in particular the effects of stochasticity on the susceptibility of the system to this spontaneous patterning, and the characteristics of the emergent structures.