Sala Seminari (Dip. Matematica).
The talk introduces and discusses some recent results on the existence of mass constrained ground states for stationary nonlinear Schrodinger equations on periodic metric graphs. Even though every metric graph is locally a one–dimensional structure, we will see how different degrees of periodicity give rise to threshold phenomena typical of higher dimensions. In doing so, direct connections between the variational problem under exam and the validity of certain functional inequalities will be pointing out, revealing the relation between periodicity and dimension.