Event Detail

Event Type: 
Department Colloquium
Date/Time: 
Monday, March 5, 2018 - 16:00 to 17:00
Location: 
Kidder 350

Speaker Info

Institution: 
University of Illinois, Chicago
Abstract: 

In this talk we will give an overview of recent developments in the modeling of hydrodynamic systems with self-organization. These models appear in a broad range of applications, from biological sciences to theories of social behavior. The common challenge in modeling such systems is to include realistic local interactions between agents and at the same time to build an analytically tractable PDE. First agent-based systems of this type appeared in seminal works of Cucker and Smale. We will walk through several refinements of the original system (on macroscopic level) and introduce the latest topological model which responds well to analysis yet exhibits the most fundamental feature of collective dynamics -- emergence of consensus. These models present new challenges to the actively developing regularity theory for fractional parabolic equations with rough drift.