1) Optimal control and controllability with state constraints.
2) Problems of unilateral dragging (Moreau's sweeping process).

Older topics:
1) Non-convex problems in set-valued analysis, differential inclusions, and calculus of variations.
2) Nonsmooth analysis and geometric measure theory, with applications to the regularity of
the minimum time function.

I can propose theses at various levels, on most topics listed in the "Aree di ricerca" part.