William Martinson

I am interested in the development and analysis of mathematical models for collective migration -- the coordinated movement of multiple individuals. This phenomenon is ubiquitous throughout biology: it plays a crucial role in successful embryonic development, for instance, as certain stem cells known as the neural crest travel throughout the embryo to help form the skeletal and nervous systems. A similar process also occurs during the formation of new blood vessels (where it is also known as angiogenesis). Even particular species of animals, such as starlings and barracuda, are known to form intricate flocking and swarming patterns when groups move together.

However, the particular means by which cells coordinate their movements are not well characterised in many biological contexts. Mathematical modelling can help supply new insight into how collective migration emerges from individual-level interactions, as it can tractably evaluate different biological hypotheses in an abstract setting, explore how certain mechanisms contribute to group behaviour, and guide the design of new experiments in collaboration with biologists. This is the goal of my research.