This volume contains the proceedings of the 1999 International Conference on Differential Equations and Mathematical Physics. The contributions selected for this volume represent some of the most important presentations by scholars from around the world on developments in this area of research. The papers cover topics in the general area of linear and nonlinear differential equations and their relation to mathematical physics, such as multiparticle Schrodinger operators, stability of matter, relativity theory, fluid dynamics, spectral and scattering theory including inverse problems.

Table of Contents:
On the Brown-Ravenhall relativistic Hamiltonian and the stability of matter by A. A. Balinsky and W. D. Evans Assessing accuracy in a numerical Einstein solver by R. Bartnik Variational principle for the limit cycle of Rayleigh's equation by R. D. Benguria and M. C. Depassier Approach to the singularity in spatially inhomogeneous cosmologies by B. K. Berger On the absolute continuity of the periodic Schrodinger and Dirac operators with magnetic potential by M. Sh. Birman and T. A. Suslina Correlations, spectral gap and log-Sobolev inequalities for unbounded spins systems by T. Bodineau and B. Helffer One dimensional regularizations of the Coulomb potential with application to atoms in strong magnetic fields by R. Brummelhuis, M. B. Ruskai, and E. Werner Construction of a solution to the semilinear elliptic equation in Chern-Simons gauge theory by D. Chae and O. Yu. Imanuvilov Approximate eigenvectors and spectral theory by M. Christ, A. Kiselev, and Y. Last The initial value problem in the large and spacetime singularities by D. Christodoulou On the kernel of $Spin^c$ Dirac operators on $\mathbb S^3$ and $\mathbb{R}^3$ by L. Erdos and J. P. Solovej Realizing holonomic constraints in classical and quantum mechanics by R. Froese and I. Herbst A combined sine-Gordon and modified Korteweg-de Vries hierarchy and its algebro-geometric solutions by F. Gesztesy and H. Holden A minimax principle for eigenvalues in spectral gaps by M. Griesemer Semiclassical dynamics and exponential asymptotics by G. A. Hagedorn and A. Joye Genericity of the band-gap structure of periodic media in the large coupling limit by R. Hempel and K. Lienau Distribution of eigenvalues in the dense point spectrum of Schrodinger operators by A. M. Hinz On the distribution of scattering resonances for asymptotically hyperbolic manifolds by P. D. Hislop The multiformity of Lifshits tails caused by random Landau Hamiltonians with repulsive impurity potentials of different decay at infinity by T. Hupfer, H. Leschke, and S. Warzel Schrodinger operator perturbed by dynamics of lower dimension by W. Karwowski and V. Koshmanenko Hyperbolic inverse problem with data on a part of the boundary by Y. V. Kurylev and M. Lassas Best Sobolev inequalities on Riemannian manifolds by Y. Li Self-energy of electrons in non-perturbative QED by E. H. Lieb and M. Loss The ground state energy of a dilute Bose gas by E. H. Lieb and J. Yngvason Trace formulae and completely integrable Hamiltonians by M. Ohmiya On the maximum and anti-maximum principles by Y. Pinchover The null condition and global existence of nonlinear elastic waves by T. C. Sideris The Hartree-Fock approximation in quantum electrodynamics-Positivity of the energy by H. Siedentop Shock-wave cosmology by J. A. Smoller and J. B. Temple On some reverse inequalities in the Segal-Bargmann space by S. B. Sontz On the initial value problem of the Toda and Kac-van Moerbeke hierarchies by G. Teschl A class of non-selfadjoint Hill's operators with analytic potentials by V. Tkachenko Regularized long wave-KP models by M. M. Tom Spectral issues for block operator matrices by C. Tretter Some fully nonlinear equations in conformal geometry by J. A. Viaclovsky $L^p - L^{\acute{p}}$ estimates for the Schrodinger equation and inverse scattering by R. Weder Stationary states of Vlasov system by G. Wolanski.