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Roman Shvydkoy, University of Illinois at Chicago, Topological models of singular Cucker-Smale dynamics
September 19, 2018 | 3:00 pm - 4:00 pm EDT
In this talk we will discuss new classes of models that seek to describe evolution of a congregation of agents based on laws of self-organization. These models appear in a broad range of applications — from biological sciences to social behavior. We focus on two long time phenomena: flocking and alignment. It has been a mathematical challenge to predict such phenomena when interactions between the agents are strictly local. We will introduce a new communication protocol based on topological rather than Euclidean distances, and use it to prove unconditional alignment even if at no specified rate.
The model includes a singular anisotropic diffusion which falls into a class of fractional parabolic equations with rough drift. We will describe some new techniques to prove regularity of such equations.
The talk is based on a recent joint work with E. Tadmor.