组织者: 邓权灵

Abstract:

Clustering behavior is ubiquitous in natural phenomena, such as birds flocking and fish swarming. In 2007, Cucker and Smale introduced the well-known Cucker-Smale model to describe the collective behavior of bird flocks. The population of birds and fish in nature is very large, therefore how to characterize its clustering behavior when the system size goes to infinity is an important issue. On the other hand, clustering behavior relies on the exchange of information among constituent elements (agents, particles), and the eigenvalues of the corresponding graph Laplacian to the consensus model under consideration provide a measure of such information exchanges. In this talk, we will discuss the clustering dynamics and spectral analysis of the infinite Cucker-Smale model from the kinetic models and infinite graph Laplacian, respectively.

Bio:

Xinyu Wang is a Postdoctoral Fellow in the Department of Mathematical Sciences at Seoul National University. His research interests include collective behavior in multi-agent systems, kinetic equations, and optimal transport. He has published research papers in journals such as Mathematische Annalen and Mathematical Models and Methods in Applied Sciences.