School on Synchronization: from collective motion to brain dynamics

Synchronization is a fundamental phenomenon in complex systems and nonlinear dynamics, driving coordinated behavior across a wide range of natural and artificial systems. From the synchronized flashing of fireflies to the coordinated oscillations in brain networks, the study of synchronization has revealed profound insights into how order emerges in interacting systems. While often associated with order and coherence, synchronization in complex networks can exhibit surprising behaviors, challenging traditional perspectives and revealing new facets of dynamical organization.In this talk, I will first review key contributions from our group to the understanding of synchronization in systems of mobile oscillators. These systems, characterized by the interplay between dynamical states and the physical motion of the oscillators, provide a rich platform to explore novel forms of synchronization.Furthermore, I will highlight the pivotal role of symmetries in shaping synchronization and its breakdown in brain networks. Our work has uncovered how symmetry-breaking mechanisms drive the emergence of localized activity patterns and how symmetry-based principles can be used to design interventions for desynchronization.