Calculus of Variations and Geometric Measure Theory

Modeling, analysis, and control of multi-agent systems across scales

created by morandott on 18 Jul 2023
modified on 22 Jul 2023

22 jan 2024 - 26 jan 2024   [open in google calendar]

Pisa: Centro De Giorgi

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.

Organizers: Giacomo Albi, Stefano Almi, Nadia Loy, Marco Morandotti, Francesco Solombrino.

Speakers: Luigi Ambrosio, Giulia Cavagnari, Annalisa Cesaroni, Young-Pil Choi, Martina Conte, Maria Rita D’Orsogna, Bertram Düring, Massimo Fornasier, Helene Frankowska, Michael Herty, Elisa Iacomini, Dante Kalise, Kevin John Painter, Lorenzo Pareschi, Benoit Perthame, Emanuela Radici, Stefano Rossi, Sui Tang, Daniela Tonon, Claudia Totzeck, Oliver Tse, Mattia Zanella, Ewelina Zatorska, Marta Zoppello.