Stochastic and Multiscale Modeling and Computation Seminar by Trevor Leslie: Questions and Philosophy of the Mathematical Theory of Collective Behavior

Speaker: Trevor Leslie, assistant professor of mathematics, University of Southern California 

Title: Questions and Philosophy of the Mathematical Theory of Collective Behavior

Abstract: I will describe in broad strokes some goals in the mathematical study of collective behavior and give examples of several relevant models.  We will discuss the multi-scale framework, inspired by the kinetic theory of gas dynamics, which is used to study some of these models.  Finally, we will discuss several possible communication rules for the Cucker--Smale system of ODE's, and how these communication rules tend to affect the dynamics.  

This will be the first talk in a several-part series.  Depending on the interests of the audience, future talks may concern the mean-field (discrete-to-kinetic) and/or kinetic-to-hydrodynamic limits, the Eulerian and Lagrangian perspectives, regularity theory for the PDE's involved, and the prediction of limiting states based on the initial data and communication rules.  These topics will be presented in the context of the Cucker--Smale and Euler alignment systems, but the focus will be on the tools involved, which are relevant to more general equations.

 

 

Stochastic and Multiscale Modeling and Computation Seminar

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