Analytical aspects of self-organization in systems of collective behavior

by Prof. ROMAN SHVYDKOY (University of Illinois at Chicago)

Thursday 8 Apr 2021, 17:00 → 18:00 Europe/Rome

GSSI

Abstract:

In this talk we will give an overview of recent advances in the field of collective behavior, and in particular alignment models. These models appear in a wide variety of applications - swarming in biological systems, social networking, opinion dynamics, etc.

One of the most challenging problems in the field is to understand emergent phenomena, such as flocking, under purely local communication protocol between agents. We will introduce new ways to handle this problem with the mathematical formulation of a topologically based fractional diffusion mechanism, a mechanism which has in fact been observed in several empirical studies, in particular, the StarFlag project run by a group of Italian experimentalists. Such models, however, present considerable technical challenges from the point of view of regularity theory,  some of which will be highlighted in the talk.