Preface This Festschrift had its origins in a conference called SimonFest held at Caltech, March 27-31, 2006, but it is not a Proceedings volume in the usual sense. Barry Simon requested that both his birthday conference and this Festschrift concentrate not so much on what the speaker or writer has done recently, but instead on reviews of the state of the art, with a focus on recent developments and open problems. While the number of speakers at Simonfest was originally limited by the number of hour slots in a full week, the contributions to this Festschrift contain a few additionally selected reviews. In the end, the bulk of the articles in this Festschrift are of this state of the art survey form with a few that instead review Barry's contributions to a particular area. In Part 1, the focus is on the areas of Quantum Field Theory, Statistical Me- chanics, Nonrelativistic Two-Body and TV-Body Quantum Systems, Resonances, Electric and Magnetic Fields, and Semiclassical Limit. Here in Part 2, the focus is on the areas of Random and Ergodic Schrodinger Operators, Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory. For a detailed preface, including a short biography of Barry Simon, we refer the reader to Part 1 of this two-volume Festschrift. We are grateful to Sergei Gelfand, Christine Thivierge, and the staff at AMS for their support throughout the preparations of this Festschrift. We also thank all authors for their contributions and the referees for their invaluable assistance. We sincerely thank the following sponsors of SimonFest for their financial support: Caltech's Center for the Mathematics of Information (CMI) Caltech's Division of Physics, Mathematics, and Astronomy International Association of Mathematical Physics (IAMP) International Union of Pure and Applied Physics (IUPAP) U.S. National Science Foundation (NSF). Percy Deift Cherie Galvez Fritz Gesztesy Peter Perry Wilhelm Schlag October 2006 ix

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