Complex systems of many interacting particles are ubiquitous in nature and account for several interesting
phenomena, ranging from gas atoms to social dynamics, passing through chemical reaction networks. A
powerful tool for the understanding of such systems and for the taming of their remarkable intrinsic
complexity is the introduction of macroscopic descriptions: particles are not seen individually anymore, but
are described through their density which, in the limit as the number of particles goes to infinity, solves a
single kinetic integro-differential equation. The Boltzmann equation and mean-field limits of particle systems
are prominent examples of this point of view, which, originating from statistical physics, has indeed proved
to be a strikingly effective instrument with a large scope of possible applications in other branches of science
and societal problems.
The mathematical challenge relates to this approach are actually manyfold, as they not only involve the
rigorous validation of the limit process, but also the effective simulation of large systems through the
introduced approximations, as well as the designing of suitable control strategies to steer the system
towards some desired state. The desired impact of these theories is not only confined to the theoretical
understanding or the computations issues of these complex systems, but aims at suggesting viable and
targeted interventions for improving real-life scenarios.
The investigation of these systems lies at the interface among modelling, analysis, probability, and numerics.
It may also require some advanced theoretical techniques which were developed independently of these
applications in contexts such as measure theory, functional analysis, or differential geometry.
The aim of this workshop is to bring together leading experts and young researchers in this fields, taking
advantage in a synergic fashion of the different backgrounds and domains of expertise. Attention will be
given both to up-to-date applications to physical, biological, and social systems, and to cutting edge
theoretical advances in the rigorous mathematical formulation of the theory, including
-- Boltzmann and mean-field descriptions;
-- well-posedness of control systems and optimality conditions;
-- particle-based optimization, and learning;
-- simulations and real-life applications;
-- abstract functional settings and tools;
-- convergence of numerical schemes.
Limited funding might be available to early registered participants. If needed, please contact Marco Morandotti at firstname.lastname@example.org, inserting “Multi-agent systems in Pisa” in the object of the email.