Describing interacting particle systems via partial differential equations and graphons

The study of large populations of interacting agents connected via a non-trivial network of connections represents a field of growing interest in Applied Mathematics. The relatively recent theory of graphons turns out to be well-adapted to model the emergence of complex networks and has been applied in several contexts by now, including mean-field systems. In this talk, we discuss how some of the key properties of graphon objects, e.g., exchangeability and labelling, are related to the study of interacting particle systems. Hopefully, this will shed some light on the behavior of systems described by partial differential equations and graphons, as the Graphon Mean-Field Game equations.