Emergent behavior in collective dynamics
Collective dynamics is driven by alignment that tend to self-organize the crowd and by different external forces that keep the crowd together. Different emerging equilibria are self-organized into clusters, flocks, tissues, parties, etc.
I will overview recent results on the hydrodynamics of large-time, large-crowd collective behavior, driven by different rules of engagement. In particular, I address the question how short-range interactions lead, over time, to the emergence of long-range patterns, comparing geometric vs. topological interactions.