abstract: In this talk we discuss Strichartz estimates on the Heisenberg group for the linear Schrödinger equations involving the sublaplacian. The Schrödinger equation on the Heisenberg group is an example of a totally non-dispersive evolution equation: for this reason the classical approach that permits to obtain Strichartz estimates from dispersive estimates is not available. Our approach, inspired by the method initiated by Tomas and Stein, is based on Fourier restriction theorems, using the non-commutative Fourier transform on the Heisenberg group. With the same techniques, we obtain also an anisotropic Strichartz estimate for the corresponding wave equation, for a larger range of indices than was previously known. Based on a joint work with Hajer Bahouri and Isabelle Gallagher.