Program of a Mini - Course “ Resonances and Threshold Singularities for Magnetic Quantum Hamiltonians ”

1. Basic facts from the spectral theory of magnetic quantum Hamilto-nians (Schrödinger, Pauli, and Dirac operators with magnetic fields): self-adjointness, gauge invariance, diamagnetic inequality, Aharonov-Casher theorem [1, 7]. Constant magnetic fields [1]. 2. Berezin-Toeplitz operators and pseudodifferential operators with con-4. Resonances for the 3D Schrödinger operator with constant magnetic field and short-range electric potential: definition, resonance-free domains , existence of infinitely many resonances near each Landau level [4]. Main asymptotic term of the resonance counting function near a given Landau level [5]. Extensions to Pauli and Dirac operators [19]. Remark: The program is meant for four lectures of approximately 90 minutes. If necessary, the program could be shortened or extended.