Analytical Aspects of Emergent Dynamics in Systems of Collective Behavior

Explore the analytical aspects of emergent dynamics in systems of collective behavior in this seminar presented by Roman Shvydkoy from the University of Illinois Chicago. Delve into the challenging problem of understanding global emergent phenomena arising from local communication between agents in alignment dynamics. Examine examples such as flock formations, opinion consensus, and leader emergence. Investigate the importance of graph-, chain-, or hydrodynamic connectivity in ensuring collective outcomes. Discover two new approaches to alignment dynamics in disconnected or weakly connected flocks: one based on topological fractional diffusion resembling the closest neighbor rule, and another utilizing random fluctuations and the hypocoercivity property for the kinetic Fokker-Planck-Alignment equation. Gain insights into this complex field of study through this comprehensive overview of the subject.