Restriction of toral eigenfunctions to curves

An interesting problem about eigenfunctions of the Laplace operator is to understand their concentration properties. In the setting of flat tori, Bourgain and Rudnick in a series of papers established uniform bounds for restriction of eigenfunctions to hypersurfaces, as well as several other beautiful results. I will present a selection of these in the two-dimensional case, where some magic happens and many technical difficulties disappear.