Title: Common nodal surfaces in the Euclidean spaces
Nodal sets are zero loci of Laplace eigenfunctions and are important for understanding
wave processes. The geometry of the nodal set of an individual eigenfunction may be very complicated and hardly can be well understood. On the other hand, simultaneous vanishing of many eigenfunctions (resonance) is an overdetermined condition and might be expected to occur only either for small or for special sets, so that in such cases discovering geometric shape of the nodal sets is possible. The talk is devoted to the above problem for hypersurfaces in the Euclidean spaces.