Abstract: n this talk, I will present several results and insights on the formation of consensus in first-order graphon dynamics, obtained in collaboration with Mario Sigalotti and Nastassia Pouradier Duteil (INRIA, Sorbonne Université). Consensus is perhaps the simplest asymptotic pattern one may wish to investigate in the context of collective motion, and has been thoroughly studied by a large number of scientists from very diverse communities. From a foundational standpoint, though, the families of results that I tend to believe stand out are the following. On the one hand, those from the engineering communities from the early 2000's, that gave very sharp conditions for consensus in general heterogeneous finite-dimensional cooperative systems. On the other, those from several mathematical communities starting in the late the 2000's concerning the meanfield limit of homogeneous cooperative systems, along with the well-posedness and fine stability analysis of the resulting PDEs. It seemed to us that a meeting point between these two worlds, namely a macroscopic theory able to support these sharp finite-dimensional results, accompanied perhaps by a finer understanding of how scalable they are and whether they can be linked to known meanfield approaches or not, was missing. To try and begin to fill this gap, we studied the formation of consensus in first-order graphon dynamics. The latter, which have been introduced quite recently, are a specific class of macroscopic approximations for many-body systems, taking the form of ODEs over Lp spaces, which (unlike the standard meanfield approach) allow to keep track of the identity of the agents, as well as of the potential heterogeneity in their interactions. In this context, the contributions that I will present shall bear on two graph(on)-theoretic quantities, with a discussion of what sort of connectivity properties they encode about the underlying graphon, and how they respectively relate to the decay of the variance and diameter of the system. These results were strongly inspired, both in their content and form, by the wonderful SIAM Review paper of 2014 by Motsch&Tadmor. I