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Mathematical Analysis, Modelling, and Applications

The activity in mathematical analysis is mainly focussed on ordinary and partial differential equations, on dynamical systems, on the calculus of variations, and on control theory. Connections of these topics with differential geometry are also developed.The activity in mathematical modelling is oriented to subjects for which the main technical tools come from mathematical analysis. The present themes are multiscale analysismechanics of materialsmicromagneticsmodelling of biological systems, and problems related to control theory.The applications of mathematics developed in this course are related to the numerical analysis of partial differential equations and of control problems. This activity is organized in collaboration with MathLab for the study of problems coming from the real world, from industrial applications, and from complex systems.

Mean field games and optimal transport techniques

Mean Field Games (MFG) systems have been introduced simultaneously in 2006 by Lasry-Lions and Huang-Caines-Malhamé to describe Nash equilibria in differential games with infinitely many players. MFG models are the simplest "stochastic control"-type models taking into account interactions between rational agents.

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