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 analysis, mechanics of materials, micromagnetics, modelling 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.

Periodic Solutions in Hamiltonian Systems

The search for periodic solutions in Hamiltonian systems is old and originated in the many body-problem of celestial mechanics. In the last decades it was tackled with success using the variational action functional. Our aim is to collect some old and more recent results, with a special emphazise on variational techniques.

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Parabolic Problems and Techniques

One of the most remarkable properties of evolutionary processes described by reaction-diffusion equations is the possibility of the eventual occurence of singularities developing from perfectly smooth data. In this short course for parabolic problems, we will discuss: