Includes bibliographical references.

Subelliptic geometry and fundamental solutions ; "Non-standard" spectral asymptotics for a two-dimensional Schrodinger operator ; Generic singularities for the steady Boussinesq equations ; On zeta functional determinant ; Some mathematical aspects of incompressible fluid mechanics ; On the microlocal regularity of the Schrodinger kernel ; Inverse scattering problems for the Schrodinger operators with external Yang-Mills potentials ; Existence and multiplicity of solutions for linear and nonlinear Dirac problems ; Stability of matter with magnetic fields ; A note on the multiplicity of surfaces with prescribed constant mean curvature ; The oblique derivative problem ; Stability of vortex solutions of the Ginzburg-Landau heat equation ; On some properties of zero sets and critical sets of solutions to elliptic equations ; Szego type theorems ; Singularity formation for nonlinear Schrodinger equation and self-focusing of laser beams ; Ginzburg-Landau equation I. Static vortices ; Littlewood-Paley estimates: Some applications to elliptic boundary value problems ; Positive commutator methods for nonlinear wave equations. Constraints on periods and exponential decay of periodic solutions ; Generalized determinants for Sturm-Liouville problems on the real line ; Spectra and eigenfunctions of laplacians ; Time dependent resonance theory and perturbations of embedded eigenvalues ; On the negative discrete spectrum of the operator \Delta _\mathcal N - \alpha V for a class of unbounded domains in mathbb R^d ; Vorticity structures in homogeneous turbulence ; Essential spectrum and O(2) symmetry of the energy operators of the Quantum systems with nonincreasing magnetic field