Talk by Roman Shvydkoy

The next seminar “Modelling of materials – theory, model reduction and efficient numerical methods” will take place next Monday (May 13, 2019) in the room K2 from 9:00 till 10:00. The series of talks will be given by Roman Shvydkoy and it will consist of three lectures, the second one will be on Thursday May 16 from 14:00 in K2 and the last one on Monday May 20 from 9:00 in K3. Please see the details below.

Speaker: Roman Shvydkoy (University of Chicago)

Title: Lectures on alignment models of collective behavior

Abstract: In this series of lectures we present basic principles of emergent dynamics in systems governed by laws of self-organization. Such systems arise in a variety of applications including biological (swarming behavior of animals), social (opinion dynamics, social networks) and technological contexts (cosmology, robotics, etc). A particular focus will be placed on the so-called Cucker-Smale models, which encode one of the simplest communication protocols that lead to two fundamental phenomena of collective action: alignment and flocking. We will start with elementary proofs of alignment in various scenarios involving local and global communications kernels, address the issues of collision between agents. 
Mean-field limit and hydrodynamic models will be presented in the second part of the lectures, and we address the problems of global well-posedness, long time behavior, and stability of flocks on the macroscopic (large crowd) level. Finally, we discuss singular and topological kernels within the same Cucker-Smale context, which have been recently introduced to demonstrate how global collective phenomena emerge from purely local communication. These models present many new challenges to the regularity theory of fractional parabolic PDEs, which we will also discuss if time permits.