Ground states on nonlinear quantum graphs

The nonlinear Schr\"odinger equation is an ubiquitous model in physics, with numerous applications in areas as divers as Bose-Einstein condensation or nonlinear optics. In many physical situations, the underlying space is essentially one dimensional and can be modeled as a metric graph, i.e. a collection of  vertices and edges with finiter or infinite lengths. The mathematical study of this type of model is very recent and is gaining an incredible momentum. In this talk, we will review some of the results concerning the existence of nonlinear Schr\"odinger ground states on graphs and present a numerical approach for their computation. This is a joint work with Christophe Besse and Romain Duboscq.