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.