Pattern Formation: preliminaries, stochastics and beyond

In this talk Dr Thomas Woolley will review the basic ideas of Alan Turing’s reaction-diffusion theory that acts as the basis of most pattern forming theories.

In particular, he will highlight a number of the theory’s shortcomings and demonstrate how these shortcomings can be dealt with. For example:

• The patterns are often not robust in the sense that perturbations to the initial conditions produce widely different outcomes. Domain growth can fix this.
• Turing systems are often applied to cases where there are very few bioactive agents and randomness becomes an issue. We can create a stochastic description of the system.
• Agents are assumed to randomly diffuse. What if the agents are intelligent? We can extend the framework to account for this.

In summary, Dr Woolley will demonstrate why a 60-year-old idea is still generating new ideas in mathematics and biology.

Dr Thomas Woolley studied mathematics at University of Oxford between 2004-2017 and is now a Lecturer in Applied Mathematics in Cardiff. Through his education he ended up specialising in mathematical biology, where his doctorate focused on understanding the pattern formation behind fish spots and zebra stripes. Alongside this research he now investigates mathematical models of stem cell movement. The hope is that by understanding how stem cells move we can influence them and, thus, speed up the healing process.