Josh graduated from the University of Bath in 2018 with an MMath, where he focused primarily on Probability Theory. He completed two summer projects with the Bath Institute for Mathematical Innovation, firstly on the Keston-Stigum theorem for discrete time branching processes, and secondly on the optimization of tensegrity structures. His final year project was on the conformal invariance of critical site percolation but he is interested in learning more about a wide variety of topics. Besides maths, Josh enjoys reading, films, squash, and knitting bad hats.

Research project title:
Hybrid methods for modelling the cell-division cycle

Supervisor(s):
Kit Yates

Project description:
Biological systems exhibit a tremendously wide variety of behaviours at many different spatial scales. While in theory, the behaviour of a system at any scale can be viewed as emergent from the behaviour of its smallest components, deriving these scale relationships is analytically intractable except in only very carefully constructed examples. Numerical methods based purely on a system’s microscopic behaviour can quickly become cost-prohibitive as the number of atomic components of a system increases. To achieve computational feasibility, different modelling regimes are used at different scales, though at the cost of information loss when using coarser representations. Josh’s work is concerned with hybrid methods, which combine multiple regimes to balance the advantages and disadvantages of each. In particular, he aims to construct a hybrid method based on a model of the cell-division cycle as a reaction-diffusion system, building upon previous hybrid methods such as the pseudo-compartment method.