By Fritz Gesztesy, Percy Deift, Cherie Galvez, Peter Perry, and Wilhelm Schlag
This Festschrift had its origins in a convention referred to as SimonFest held at Caltech, March 27-31, 2006, to honor Barry Simon's sixtieth birthday. it's not a complaints quantity within the ordinary experience because the emphasis of the vast majority of the contributions is on reports of the cutting-edge of yes fields, with specific specialise in fresh advancements and open difficulties. the majority of the articles during this Festschrift are of this survey shape, and some evaluate Simon's contributions to a selected region. half 1 comprises surveys within the components of Quantum box conception, Statistical Mechanics, Nonrelativistic Two-Body and $N$-Body Quantum structures, Resonances, Quantum Mechanics with electrical and Magnetic Fields, and the Semiclassical restrict. half 2 comprises surveys within the components of Random and Ergodic SchrÃ¶dinger Operators, Singular non-stop Spectrum, Orthogonal Polynomials, and Inverse Spectral thought. in numerous situations, this choice of surveys portrays either the heritage of a topic and its present state-of-the-art. Exhaustive lists of references increase the presentation provided in those surveys. a considerable a part of the contributions to this Festschrift are survey articles at the cutting-edge of sure components with distinct emphasis on open difficulties. this can profit graduate scholars in addition to researchers who are looking to get a short, but entire advent into a space lined during this quantity.