Trygve Karper: On some biological models of self-organization

In nature, groups of individuals organize globally using only local information. For instance, in a school of fish, there are no external forces to coordinate the group, no leader to guide them. Several mathematical models have been proposed to describe self-organization. In this talk, we will consider two of the most famous models; the Keller-Segel model for bacterial chemotaxis and the Cucker-Smale model for flocking. The emphasis will be on recent mathematical results and remaining open questions. Starting from the microscopic description on particle level, we will discuss the derivation of mesoscopic and macroscopic models at the continuum level. Since the motivation for deriving continuum models is largely numerical, we will also discuss distinct numerical challenges with the resulting models.