## Szabolcs Zakany

I obtained my Master degree (2014) and my PhD (2019) in Physics from the University of Geneva, under the supervision of Professor Marcos Mariño. I studied mathematical aspects of string theories, in particular a duality between a family of topological strings and the spectral theory of certain quantum mechanical operators. This duality leads to a consistent non-perturbative realisation of this family of topological strings, whereas in general string theories are only defined perturbatively in the string coupling.

In 2019, I switched my domain of studies and joined, as a postdoc, the Laboratory of Artificial and Natural Evolution (LANE) of Professor Michel Milinkovitch in the Biology section of the University of Geneva. The LANE’s motivation is to understand the diversity of complex life forms through a multidisciplinary approach involving developmental and evolutionary biology, as well as biological physics and mathematical modelling. In particular, we study the development and evolution of skin appendages and skin colour patterning in vertebrates, with a focus on non-model species.

Friday April 21st

### Skin colour patterning: the example of the ocellated lizard

The colour patterning of animal skin is a striking example of how living matter spatially self-organises. In most cases, this process happens during embryogenesis. However, in the case of the ocellated lizard (Timon lepidus), the adult pattern is established post-hatching, thus giving a great opportunity to study the dynamics of skin patterning in vivo. The final distribution of green and black skin-scales arranged in a ‘labyrinthine’ pattern is reached through a series of scale colour switches, which can be modelled in different ways. First, we consider a phenomenological model in terms of a ‘stochastic cellular automaton’ where the skin-scales provide the spatial discretisation. This description gives an interesting link with the Ising model: in this picture the lizard pattern is a frustrated anti-ferromagnet. Second, we consider an effective model of interactions between chromatophores which takes the form of a reaction-diffusion system in a domain with varying thickness, representing skin-scales. In this model, the patterning is the consequence of a Turing instability, and the peculiar scale-by-scale colouring and colour switching is a consequence of the skin-scale geometry. An extra feature of the model is that the precise colour of a green (or black) skin-scale has a subtle dependence on the number of nearest neighbour skin-scales which have the same colour. This prediction could be successfully verified in real lizards.