Roman Shvydkoy
University of Illinois at Chicago

Abstract: Emergence is a phenomenon of formation of collective outcomes in systems where communications between agents has local range. In dynamics of swarms such outcomes often represent a globally aligned flock or congregation of aligned clusters.  The classical result of Cucker and Smale states that alignment is unconditional in flocks that have global communication with non-integrable radial tails. Proving a similar statement for purely local interactions presents a major mathematical challenge.  In this talk we will overview three programs of research directed on understanding the emergent phenomena: hydrodynamic topological interactions,  kinetic approach based on hypocoercivity, and spectral energy method.  We present a novel framework based on the concept of environmental averaging which allows us to obtain coercivity estimates leading to new flocking results.