As part of the 6th Scottish PDE Colloquium to be held at the University of Edinburgh May 31st and June 1st, there will be a 2-hour MIGSAA colloquium about PDEs applied to the social sciences aimed at PhD students. See details below:
Time: May 31st, 14:30-17:00, JCMB
Location: Lecture Theatre A
On Boltzmann-type equations in socio-economic applications
Marie-Therese Wolfram (University of Warwick)
Kinetic equations have become an indispensable tool to provide a quantitative description of diverse phenomena, such as semi-conductors, plasma physics, price and opinion formation, and more recently animal herding and pedestrian dynamics.
In this talk we discuss how kinetic or so-called Boltzmann type models, can be used to describe the dynamics of many interacting particle systems in pedestrian dynamics and opinion formation. Starting with the microscopic interaction laws, we derive the corresponding Boltzmann-type equations and discuss the behavior of solutions in different limits. Numerical simulations complete the picture of the rich dynamics and confirm the emergence of complex pattern, such as lane formation in bidirectional flows.