Spectral theory of confining magnetic fields via symplectic geometry

I will present recent results giving precise eigenvalue asymptotics for the magnetic Laplacian for large magnetic fields (semiclassical limit), in the case of a confining, non-uniform field, in dimensions 2 and 3. The essential ingredient is the symplectic geometry of the zero-energy manifold in the magnetic phase space, and the quantization of the various oscillations of the Hamiltonian flow for long times.

This is joint work with B. Helffer, Y. Kordyukov and N. Raymond.