Partial Differential Equations and Mathematical Physics

On perturbation of embedded eigenvalues. - Blowup of classical solutions of nonlinear hyperbolic equations: a survey of recent results. - Global time decay of the amplitude of a reflected wave. - Weyl quantization and Fourier integral operators. - The local index theorem without smoothness. - How ideas from microlocal analysis can be applied in 2-D fluid mechanics. - Lp spectral independence for certain uniformly elliptic operators. - Trace asymptotics via almost analytic extensions. - A microlocal version of concentration-compactness. - Complete heat trace resolvent and zeta expansions for general Atiyah-Patodi-Singer problems. - Semi-classical analysis for the transfer operator: WKB constructions in dimension 1. - Several recent results in nonlinear geometric optics. - Stabilization of the wave equation by the boundary. - About small-power semilinear wave equations. - The Faddeev approach to inverse scattering from a micro-local perspective. - Fibrations compactifications and algebras of pseudodifferential operators. - Degree theory beyond continuous maps. - On the Weyl formula for obstacles. - On the asymptotic completeness for particles in constant electromagnetic fields. - The size of atoms in Hartree-Fock theory. - Holomorphic extension of CR functions: a survey. - Local solvability in a class of overdetermined systems of linear PDE. - Neumann resonances in linear elasticity. Language: English