Semiclassical asymptotics of the spectral function of the magnetic Schrodinger operator

In the talk, we discuss asymptotic spectral properties of the Schrodinger operator with uniformly bounded magnetic field in Euclidean space in the semiclassical limit. We give a rough asymptotic description of its spectrum and describe the full off-diagonal asymptotic expansion of its smoothed spectral function. As consequences, we obtain the semiclassical trace formula and an asymptotic localization property of the spectral function in the case when the magnetic field has maximal rank.