In this paper we introduce the Mathematical Desk for Italian Industry, a project based on applied and industrial mathematics developed by a team of researchers from the Italian National Research Council in collaboration with two major Italian associations for applied mathematics, SIMAI and AIRO.

This work reports on vehicular traffic modeling by methods of the discrete kinetic theory. The purpose is to detail a reference mathematical framework for some discrete velocity kinetic models recently introduced in the literature, which proved capable of reproducing interesting traffic phenomena without using experimental information as modeling assumptions. To this end, we firstly derive a general discrete velocity kinetic framework with binary nonlocal interactions.

In this paper we propose a classification of crowd models in built environments based on the assumed pedestrian ability to foresee the movements of other walkers. At the same time, we introduce a new family of macroscopic models, which make it possible to tune the degree of predictiveness of the individuals.

The modeling of various physical questions in plasma kinetics and heat conduction lead to nonlinear boundary value problems involving a nonlocal operator, such as the integral of the unknown solution, which depends on the entire function in the domain rather than at a single point. This talk concerns a particular nonlocal boundary value problem recently studied in [1] by J.R.Cannon and D.J.Galiffa, who proposed a numerical method based on an interval-halving scheme.