Differential Games Towards Modeling Complexity and Social Behaviors Looking for the Black Swan
by Nicola Bellomo, Department of Mathematical Sciences, Politecnico di Torino
Huxley 140, 16:00-17:00
This lecture presents a modeling approach of systems of interacting individuals viewed as a large living, hence complex, system. The approach is based on methods of the mathematical kinetic theory for active particles, where the main difference with respect to classical methods is that interactions between particles are described by stochastic evolutive games rather than by deterministic causality principles.
Mathematical tools include a detailed analysis of the complexity features of the systems under consideration to be properly inserted into mathematical structures. Models describe the time and space dynamics of a probability distribution over the micro-state of each interacting entities. Subsequently some applications are proposed focusing on Darwinian evolution of multicellular systems in the immune competition, social dynamics including welfare distribution and political competition, and crowd dynamics.
The presentation constantly refers to the modeling complex large systems of individuals interacting in a non-linear manner. These systems, as known, are difficult to model and understand at a global level. Namely, emerging collective behaviors of the overall system cannot be related only on the knowledge of the dynamics of their individual elements.
Some perspective ideas and hints towards the modeling and collective ”swarm” intelligence will be given. In some cases, the swarm may lead to not predictable events, namely the so-called black swan.
Well-posedness of the 3D Prandtl Layer Equations by Tong Yang, Department of mathematics City university of Hong Kong
Huxley 140, 17:00-18:00
The well-posedness of the 3D Prandtl layer equations is studied both locally and globally in time under some constraint on its flow structure. It reveals that the classical Burgers equation plays an important role in the analysis. And the monotonicity condition on the velocity and the favorable conidtion on pressure are illustrated in the 3D setting. Moreover, the linear stability of this structured flow is justified. This is a joint work with Chengjie Liu and Yaguang Wang.