Preface -- Lower bounds for sojourn time in a simple shape resonance model -- Spectral properties for Hamiltonians of weak interactions -- Magnetic Laplacian in sharp three-dimensional cones -- Spectral clusters for magnetic exterior problems -- The spectral shift function and the Witten index -- Stahl's theorem (aka BMV conjecture): insights and intuition on its proof -- Some estimates regarding integrated density of states for random Schrödinger operator with decaying random potentials -- Boundary values of resolvents of self-adjoint operators in Krein spaces and applications to the Klein-Gordon equation -- Levinson's theorem: an index theorem in scattering theory -- Counting function of magnetic resonances for non-definite sign perturbations -- Harmonic analysis and random Schrödinger operators.