Recently, there has been an increasing interest from the community in real-life complex system modeling. The most popular example is provided by systems where the number of agents is so large, that only a statistical description (reminiscent to the statistical mechanics description of systems in thermodynamics) turns out to be viable. The usual way to model such kind of systems is to choose a measure space over the underlying Euclidean space as new state space: the measure of a set will give an estimate of the agent present in that set. The peculiarity of such and infinite-dimensional space, and the connection with optimal transport theory, lead to a very rich mathematical structure. In this talk we provide some recent results obtained in optimal control of multi-agent systems, among which we mention a characterization of the value function for some optimal control problems by means of a suitable infinite-dimensional Hamilton-Jacobi equation. Applications will be presented, together with planned future developments.

Bio: Antonio Marigonda, born in Rome, Italy on 30th Nov 1977, obtained his Ph.D. in Mathematics in 2006 at the University of Padova, Italy with a thesis entitled “Differentiability properties for a class of non-Lipschitz functions and applications” under the supervision of prof. Giovanni Colombo. After two postdoc periods at the University of Roma “La Sapienza” and at the University of Pavia, he obtained a permanent position as Researcher at the University of Verona. His main scientific interests concern the broad field of Mathematical Theory of Optimization, namely Nonsmooth Analysis, Geometric Measure Theory, Control Theory and Optimization, Viscosity solutions of Hamilton–Jacobi equations, Optimal Transportation Theory and application to models in Economics, Finance and social sciences.

Dr. Marigonda is a candidate for the Director of Financial Mathematics and a Faculty position in mathematics.