The physics of confluent tissues and the Smale's 17th problem
Mon, Aug. 28th 2023, 11:00-12:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
Models of confluent tissues are constructed out of tessellation of space into cells. Metabolic reasons are invoked to constrain the volume and surface of the cells. Depending on the imposed shape, the resulting tissue can be solid or liquid with a phase transition, also called rigidity transition, in between. I will discuss a simple continuous constraint satisfaction problem with equality constraints and show that it displays the same phase diagram as models of tissues. The model consists in a simple overparametrized set of random non-linear equations which must be solved simultaneously. I will discuss the zero temperature limit of a carefully defined Gibbs measure and use it to compute the satisfiability transition point, which corresponds to the rigidity transition in confluent tissues. If time permits I will also discuss the quantum version of the model, and show that quantum fluctuations may promote glassiness instead of suppressing it.