I will present several results regarding magnetic Laplacians on closed Riemannian manifolds. The first part of the presentation will focus on hyperbolic surfaces and constant magnetic intensity. In this setting, the spectrum is regular with high multiplicities up to a critical energy level, above which it becomes chaotic. In joint work with T. Lefeuvre, we established a quantitative unique quantum ergodicity property at this critical level. In the second part, I will discuss Landau levels for non-degenerate magnetic fields. These levels are clusters of eigenvalues at the bottom of the spectrum, each cluster corresponding to an effective Berezin-Toeplitz operator.
