|Abstract:|| Since the pioneering works of A. Einstein, M. von Smoluchowski, and P. Langevin, stochastic processes and the related Fokker-Planck equations have been used to model irregular motion in different situation. These equations are also considered to be adequate for modelling the motion of one pedestrian and of a crowd of people under certain circumstances. Therefore they can play a central role in the design of control strategies for different purposes as well as in the analysis and calibration of microscopic models of pedestrian interaction. The purpose of this talk is to review some mathematical results in this field, which includes different modelling issues concerning the optimal control of a single pedestrian subject to perturbation, the development of a new framework for pedestrians' avoidance dynamics based on the formulation of a Nash game, and a new approach to the analysis of superresolution 2D images of moving molecules on a cell membrane to obtain quantitative results on the organization of the membrane and on the interaction between the molecules.
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