Trace formula for the magnetic Laplacian

Given a Riemannian manifold equipped with a magnetic field 2-form, the associated magnetic Laplacian is the Schroedinger operator with magnetic field and vanishing electric potential. In this talk, we will discuss the Guillemin–Uribe trace formula, which relates some asymptotic spectral invariants of the magnetic Laplacian with geometric and dynamical invariants of the associated magnetic geodesic flow. First, we will explain the formula. Then we will describe concrete examples of its computation for two-dimensional constant curvature surfaces with constant magnetic fields and for the Katok example.
This is joint work with Iskander A. Taimanov.