This Festschrift had its origins in a conference called SimonFest held at Caltech, March 27-31, 2006, to honor Barry Simon's 60th birthday. It is not a proceedings volume in the usual sense since the emphasis of the majority of the contributions is on reviews of the state of the art of certain fields, with particular focus on recent developments and open problems. The bulk of the articles in this Festschrift are of this survey form, and a few review Simon's contributions to a particular area. Part 1 contains surveys in the areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic Two-Body and $N$-Body Quantum Systems, Resonances, Quantum Mechanics with Electric and Magnetic Fields, and the Semiclassical Limit. Part 2 contains surveys in the areas of Random and Ergodic Schrodinger Operators, Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory. In several cases, this collection of surveys portrays both the history of a subject and its current state of the art. A substantial part of the contributions to this Festschrift are survey articles on the state of the art of certain areas with special emphasis on open problems. This will benefit graduate students as well as researchers who want to get a quick, yet comprehensive introduction into an area covered in this volume.
Part I: Quantum field theory, statistical mechanics: Perspectives in statistical mechanics by M. Aizenman Coherent infrared representations in non-relativistic QED by T. Chen and J. Frohlich Quantum spin systems after DLS 1978 by B. Nachtergaele Barry Simon's contributions to quantum field theory by L. Rosen Nonrelativistic two-body and $N$-body quantum systems, resonances: Isoperimetric inequalities for eigenvalues of the Laplacian by M. S. Ashbaugh and R. D. Benguria Non-self-adjoint operators and pseudospectra by E. B. Davies Barry Simon's contribution to non-relativistic quantum mechanics: Two-body and $N$-body Schrodinger operators and resonances by R. Froese $N$-body quantum scattering and quantum resonances: An overview by C. Gerard Mathematical analysis of Born-Oppenheimer approximations by G. A. Hagedorn and A. Joye Perturbation theory and atomic resonances since Schrodinger's time by E. M. Harrell II On a theorem for quantum mechanical scattering theory by A. Lenard Analytic criteria in the qualitative spectral analysis of the Schrodinger operator by V. Maz'ya The spectral geometry of geometrically finite hyperbolic manifolds by P. Perry Topics in the theory of positive solutions of second-order elliptic and parabolic partial differential equations by Y. Pinchover Complex scaling in atomic physics: A staging ground for experimental mathematics and for extracting physics from otherwise impossible computations by W. P. Reinhardt Recent results on the Bethe-Sommerfeld conjecture by A. V. Sobolev Electric and magnetic fields, semiclassical limit: Recent developments in quantum mechanics with magnetic fields by L. Erdos Aspects of the integer quantum Hall effect by G. M. Graf Barry Simon's work on electric and magnetic fields and the semi-classical limit by I. W. Herbst Some bound state problems in quantum mechanics by D. Hundertmark Part II: Random and ergodic Schrodinger operators, singular continuous spectrum: A new approach to spectral gap problems by J. Bourgain Strictly ergodic subshifts and associated operators by D. Damanik Lyapunov exponents and spectral analysis of ergodic Schrodinger operators: A survey of Kotani theory and its applications by D. Damanik Spectral properties of Schrodinger operators with decaying potentials by S. A. Denisov and A. Kiselev On the formation of gaps in the spectrum of Schrodinger operators with quasi-periodic potentials by M. Goldstein and W. Schlag Ergodic Schrodinger operators (on one foot) by S. Jitomirskaya The integrated density of states for random Schrodinger operators by W. Kirsch and B. Metzger Exotic spectra: A review of Barry Simon's central contributions by Y. Last Orthogonal polynomials, inverse spectral theory: Riemann-Hilbert methods in the theory of orthogonal polynomials by P. Deift Inverse spectral theory as influenced by Barry Simon by F. Gesztesy Orthogonal polynomials: From Jacobi to Simon by L. Golinskii and V. Totik Orthogonal polynomials: The first minutes by S. Khrushchev Spectral theory via sum rules by R. Killip Barry Simon's list of publications by F. Gesztesy, P. Deift, C. Galvez, P. Perry, and W. Schlag.
