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 aparticular 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 andErgodic 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 comprehensiveintroduction into an area covered in this volume.

This volume contains the proceedings of the OTAMP 2008 (Operator Theory, Analysis and Mathematical Physics) conference held at the Mathematical Research and Conference Center in Bedlewo near Poznan. It is composed of original research articles describing important results presented at the conference, some with extended review sections, as well as presentations by young researchers. Special sessions were devoted to random and quasi-periodic differential operators, orthogonal polynomials, Jacobi and CMV matrices, and quantum graphs. This volume also reflects new trends in spectral theory, where much emphasis is given to operators with magnetic fields and non-self-adjoint problems. The book is geared towards scientists from advanced undergraduate students to researchers interested in the recent development on the borderline between operator theory and mathematical physics, especially spectral theory for Schrödinger operators and Jacobi matrices.

This volume consists of a long monographic paper by J. Hoffmann-Jorgensen and a number of shorter research papers and survey articles covering different aspects of functional analysis and its application to probability theory and differential equations.

"The book under review is a reprint of Mumford's famous Harvard lecture notes, widely used by the few past generations of algebraic geometers. Springer-Verlag has done the mathematical community a service by making these notes available once again.... The informal style and frequency of examples make the book an excellent text." (Mathematical Reviews)

This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.

This book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. The book is intended for researchers and students of algebraic Lie theory, as well as for other researchers who are seeking explicit realizations of algebras or modules. It will probably be more useful as a resource to be dipped into, than as a text to be worked straight through.

Annotation Contents: G. Benarous: Noyau de la chaleur hypoelliptique et géométrie sous-riemannienne.- M. Fukushima: On two Classes of Smooth Measures for Symmetric Markov Processes.- T. Funaki: The Hydrodynamical Limit for Scalar Ginzburg-Landau Model on R.- N. Ikeda, S. Kusuoka: Short time Asymptotics for Fundamental Solutions of Diffusion Equations.- K. Ito: Malliavin Calculus on a Segal Space.- Y. Kasahara, M. Maejima: Weak Convergence of Functionals of Point Processes on Rd.- Y. Katznelson, P. Malliavin: Image des Points critiques d'une application régulière.- S. Kusuoka: Degree Theorem in Certain Wiener Riemannian Manifolds.- R. Leandre: Applications quantitatives et géométrique du calcul de Malliavin.- Y. Le Jan: On the Fock Space Representation of Occupations Times for non Reversible Markov Processes.- M. Metivier, M. Viot: On Weak Solutions of Stochastic Partial Differential Equations.- P.A. Meyer: Une remarque sur les Chaos de Wiener.- H. Tanaka: Limit Theorem for One-Dimensional Diffusion Process in Brownian Environment.- H. Uemura, S. Watanabe: Diffusion Processes and Heat Kernels on Certain Nilpotent Groups.