A fascinating aspect of collective dynamics is self-organization of small scale interactions into high-order structures with larger-scale patterns. It is a characteristic feature of “social particles” which actively probe the environment and emerge into clusters. In different contexts these clusters take the form of flocks, swarms, consensus, synchronized states etc.
In this talk I will survey recent mathematical developments in collective dynamics, driven by alignment which reflects the tendency of steering towards average headings. Alignment protocols are governed by different classes of pairwise communication kernels, and a main question of interest is how different kernels affect the long-time, large-crowd dynamics. We ask how short-range interactions can affect the emergence of large-scale patterns, we discuss how graph connectivity dictates the emergent behavior of multi-species dynamics, and we show that the role of pressure away thermal equilibrium is overtaken by alignment.