Critical points of eigenfunctions

On a closed Riemannian manifold, the Courant nodal domain theorem gives an upper bound on the number of nodal domains of n-th eigenfunction of the Laplacian. In contrast to that, there does not exist such bound on the number of isolated critical points of an eigenfunction. I will try to sketch a proof of the existence of a Riemannian metric on the 2-dimensional torus, whose Laplacian has infinitely many eigenfunctions, each of which has infinitely many isolated critical points. Based on a joint work with A. Logunov and M. Sodin.