On the Schrodinger operator with white noise potential in dimensions 1, 2 and 3.

I will consider the Schrodinger operator obtained by perturbing the Laplacian with a white noise in dimensions 1, 2 and 3. I will review the construction (finite and infinite volume) and several spectral properties of this operator (statistics of the eigenvalues, localisation/delocalisation of the eigenfunctions, identification of the spectrum). Based on joint works with Laure Dumaz (ENS Paris) and Yueh-Sheng Hsu (Paris-Dauphine).