On February 9, 2010 Pierre Degond (CNRS) will be delivering a lecture entitled “Some mathematical problems related to the modeling of Complex Systems “.

Location: 2237 French Family Science Center

Time: 4:30pm

Abstract: Complex systems consist of a large number of mutually interacting agents without leader. Quite often, each agent has only access to limited information (usually about the state of the neighbouring agents). In spite of this, the system as a whole exhibits large scale spatio-temporal coordinated structures such as congestions, waves, oscillations, etc. Some examples of such systems come from traffic problems (cars on highways, pedestrians in corridors or terminals, goods on economical chains). Other examples originate from socially interacting biological entities (insect swarms, fish schools, sheep herds, organs or tumors, etc.). The self-organization behavior is not directed encoded in the local interactions between individuals and emerges when the number of agents is large. After presenting some examples, we will review a certain number of the mathematical problems posed by these systems and in particular the possibility of describing them as a ‘continuum’ or a fluid. This problem is related to the so-called chaos assumption which is the cornerstone of classical statistical mechanics and which states that in a large system, particles are nearly statistically independent.