Mathematical challenges in collective dynamics and self-organization

Nom de l'orateur
Pierre Degond
Etablissement de l'orateur
Imperial College London
Date et heure de l'exposé
Lieu de l'exposé
salle de séminaire

Most living or social systems consist of a large number of agents interacting through elementary rules involving only neighbouring agents. In spite of their simplicity, these interactions drive the system towards a self-organized coherent collective behavior. The emergence of collective dynamics poses many mathematical challenges which will be outlined in this talk. We will use the example of the Vicsek model (in which self-propelled particles interact through local alignment) to show how the loss of conservations and the analysis of phase transitions can be apprehended. Examples of applications, notably to sperm-cell collective dynamics will be presented.