Abstract: I will describe some recent results on the fine structure of eigenfunctions of the Laplacian on tori. The results concern the structure of the nodal sets (i.e. the locus of points where the function vanishes) and L^2 bounds for the restriction of the eigenfunctions to curves. I will describe how these issues connect with purely arithmetic problems on the representations of integers as sums of two squares and the distribution of the corresponding lattice points on arcs of circles. Several of these lattice point problems are still open. (Joint work with Jean Bourgain)

Coffee will be served at 12:00 before the lecture
at Schreiber building 006