Plenária 01: Dante Kalise, Imperial College of London, Reino Unido

Título: From Particles to Populations: Computational Methods for Controlling Densities Across Scales 
 

Resumo: The mathematical modeling and control of multi-agent systems is of paramount importance across several areas, ranging from statistical physics to economics, biology, and artificial intelligence. This talk explores computational and variational approaches to density control problems that bridge microscopic particle dynamics and macroscopic population behaviors. We examine recent advances in the optimal control of Fokker-Planck equations, highlighting how these techniques enable the steering of probability distributions through complex state spaces. The discussion extends to mean field control and games, where strategic interactions between agents lead to emergent collective behaviors that can be understood through the lens of non-local equations. We will highlight further connections to optimal transport, Schrödinger bridges, and global optimization. Throughout the talk, we illustrate these methods with computational examples drawn from diverse applications, including crowd dynamics, opinion formation, resource allocation, and robotic swarm control. We conclude by discussing open challenges and promising research directions at the intersection of control theory, statistical physics, and computational mathematics.