On the problem of emergence arising in hydrodynamic systems of collective behavior

 Speaker: Roman Shvydkoy (University of Illinois Chicago)

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.

Time: January 27, 2023 2:30pm-3:30pm
Location: LeConte 440
Host: Changhui Tan