Mathematical Aspects of Collective Dynamics:
Kinetic Description and Fractional Diffusion

Alignment in Cucker-Smale dynamics on the circle

Roman Shvydkoy

University of Illinois at Chicago


We will discuss recent joint results with Helge Dietert on alignment properties of Cucker-Smale type systems. Specifically we prove that for any local communication kernel (singular or smooth) the solutions to the system align algebraically fast. The result holds in both discrete and continuous cases, and the proof is based on a novel construction of a corrector to the classical energy balance law. We will also discuss an alternative dynamical approach to the problem.