Mathematics

A fascinating aspect in collective dynamics is self-organization.The dynamics is dictated by a balance of intrinsic characteristics that prefer to persist in clusters, social aspects of engagement --- alignment and anticipation that tend to self-organize, and different external forces that keep the crowd together.We will overview recent results on the hydrodynamics of large-time, large-crowd collective behavior, driven by different “rules of engagement”. In particular, we address the question how short-range interactions lead, over time, to the emergence of long-range patterns, comparing geometric vs. topological interactions.