Have you ever wondered how from the fertilised egg that divides into two cells and then into four and so on, such a variety of tissues appear? This is what developmental biology studies and, in particular, cell differentiation is the process by which unspecialised cells adopt and maintain a particular pattern of gene activity and thus become a different cell type. It is a key stage of development and its understanding could help, for instance, in regenerative medicine.
In this talk I will explain a new geometric approach to the modelling of these processes by taking advantage of catastrophe theory. It is possible to classify a rich class of dynamical systems and the bifurcations between them using singularity theory, which allows us to deeply understand the system. In particular, I will illustrate this by a model of vulval development in C. elegans. Defining a catastrophe manifold for the model and mapping signals into the parameters, I will show that we can reproduce the topology of vulval development studied.