Stochastic Differential Games and Kinetic Theory Toward the Modeling of Behavioral Social Crowds

Nicola Bellomo
King Abdullaziz University, Saudi Arabia --- Politecnico di Torino
Friday 12th February 2016
Aula Seminari Saleri, VI PIANO MOX- Dipartimento di Matematica, POLITECNICO DI MILANO
This lecture aims at providing an answer that can be given to the following five key questions: 1) Why a crowd is a \social, hence complex," system? 2) How mathematical sciences can contribute to understand the \behavioral dynamics of crowds"? 3) How the crowd behaves in extreme situations such as panic and how models can depict them? 4) Can a crowd be subject to large deviations (black swan)? 5) By which mathematical tools multiscale features of a crowd can be treated? The answer to the key question takes advantage of recent research activity documented in the five titles in the bibliography. The answer opens to challenging research perspectives. [1] B.N. and C. Dogb´e, On the modeling of traffic and crowds: A survey of models, speculations,and perspectives, SIAM Rev., 53(3), (2011), 409–463. [2] B.N., Bellouquid A., and Knopoff D., From the micro-scale to collective crowd dynamics, SIAM Multiscale Model. Simul., 11(3) (2013), 943–963. [4] B.N. and Gibelli L., Toward a mathematical theory of behavioral-social dynamics for pedestrian crowds, Math. Models Methods Appl. Sci., 25 2417-2437, (2015). [5] B.N. and Bellouquid A., On multiscale models of pedestrian crowds - From mesoscopic to macroscopic, Comm. Math. Sci., 13(7) 1649–1664, (2015).