Talk by Julien Royer

In this talk we will discuss a recent result about the local energy decay for the Schrödinger equation in an asymptotically Euclidean setting. More precisely, we will focus on the contribution of low frequency, whose behavior is given by the resolvent of the Laplacian near 0. After a review of some results about the damped wave equation, we will see how some ideas developed to deal with a non-selfadjoint operator can be used to improve what is known in a purely conservative setting.