Complex phenomena represent an inexhaustible source of modeling challenges. Thanks to the advances of the last fifteen years in graph theory, it is now possible to mathematically tackle the study of interacting particle systems on non-trivial networks. In this new framework, the connections among the particles are encoded in a general graph sequence and one is interested in modeling the population behavior, as the number of particles tends to infinity. This exposé will focus on the key mathematical results of the last five years, in the case where the particle system is defined by coupled differential equations. A special emphasis will be put on the limit description, an infinite system of Fokker-Planck equations coupled by means of a graphon.
Bio: Fabio Coppini has just finished a doctoral program in the Laboratoire de Probabilités Statistique et Modélisation in Université de Paris, under the supervision of Professor Giambattista Giacomin. His thesis focuses on linking classical results on interacting particle systems to the new tools coming from graph theory. Before, he obtained a Master in Pure Mathematics in the University of Florence (Italy).