Spectral Theory and Mathematical Physics

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 Schroedingeroperator 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 Schroedinger operators.

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• Física Matemática
• Análise funcional e transforma
• Cálculo diferencial e equações

ergodic quantum Hamiltonians;magnetic Schroedinger operators;quantum field theory;scattering theory;semiclassical and microlocal analysis;spectral shift function and quantum resonances;partial differential equations