This volume presents the proceedings of the 9th International Conference on Differential Equations and Mathematical Physics. It contains 29 research and survey papers contributed by conference participants. The conference provided researchers a forum to present and discuss their recent results in a broad range of areas encompassing the theory of differential equations and their applications in mathematical physics.Papers in this volume represent some of the most interesting results and the major areas of research that were covered, including spectral theory with applications to non-relativistic and relativistic quantum mechanics, including time-dependent and random potential, resonances, many body systems, pseudo differential operators and quantum dynamics, inverse spectral and scattering problems, the theory of linear and nonlinear partial differential equations with applications in fluid dynamics, conservation laws and numerical simulations, as well as equilibrium and non equilibrium statistical mechanics. The volume is intended for graduate students and researchers interested in mathematical physics.
Zero modes of Pauli and Weyl-Dirac operators by A. A. Balinsky and W. D. Evans The Lane-Emden equation revisited by R. D. Benguria A Paley-Wiener theorem with applications to inverse spectral theory by C. Bennewitz Zero-free regions for Jost functions: The Bessel case by B. M. Brown and M. S. P. Eastham Concentration in solutions to hyperbolic conservation laws by G.-Q. Chen Local and global continuity of the integrated density of states by J.-M. Combes, P. D. Hislop, and F. Klopp Transition to the continuum of a particle in time-periodic potentials by O. Costin, R. D. Costin, and J. L. Lebowitz Quantum dynamical bounds for one-dimensional quasicrystals by D. Damanik Lower order terms in Szego theorems on Zoll manifolds by D. Gioev Solution error models for uncertainty quantification by J. Glimm, S. Hou, Y.-H. Lee, D. H. Sharp, and K. Ye Instantaneous blow up by J. A. Goldstein and I. Kombe Simplified semiclassical propagation estimates by G. A. Hagedorn Resolvent expansions and trace regularizations for Schrodinger operators by M. Hitrik and I. Polterovich A note on the entropy production formula by V. Jaksic and C.-A. Pillet Existence and uniqueness of solutions to the operator Riccati equation. A geometric approach by V. Kostrykin, K. A. Makarov, and A. K. Motovilov Asymptotics of spectra of Neumann Laplacians in thin domains by P. Kuchment and H. Zeng Absolutely continuous spectrum of matrix valued Schrodinger operators by A. Laptev and O. Safronov Ergodic theory and discrete one-dimensional random Schrodinger operators: Uniform existence of the Lyapunov exponent by D. Lenz Bose-Einstein condensation of dilute gases in traps by E. H. Lieb and R. Seiringer On the dynamics of interfaces in the ferromagnetic XXZ chain under weak perturbations by B. Nachtergaele, W. L. Spitzer, and S. Starr Bounds for sums of powers of eigenvalues of Schrodinger operators via the commutation method by N. Pavlovic Statistical mechanics of anharmonic lattices by L. Rey-Bellet The essential spectrum of the linearized 2d Euler operator is a vertical band by R. Shvidkoy and Y. Latushkin New coherent states and a new proof of the Scott correction by J. P. Solovej and W. L. Spitzer Remark on weak solutions of stationary conduction-convection problems by B. Su Spectrum of 1-d selfadjoint periodic differential operator of order 4 by V. Tkachenko BV estimates for $n x n$ systems of conservation laws by K. Trivisa The time-dependent approach to inverse scattering by R. Weder Blowup in hyperbolic conservation laws by R. Young.