This volume surveys the spectral properties of the spin Dirac operator. After a brief introduction to spin geometry, we present the main known estimates for Dirac eigenvalues on compact manifolds with or without boundaries. We give examples where the spectrum can be made explicit and present a chapter dealing with the non-compact setting. The methods mostly involve elementary analytical techniques and are therefore accessible for Master students entering the subject. A complete and updated list of references is also included.

This volume features papers presented at the 7th Conference on Quark Confinement and the Hadron Spectrum. It covers the up-to-date research done in the physics of quarks and their role as ultimate constituents of matter. It will be of interest to all theoreticians and experimentalists working in these areas.

This book provides an update on our understanding of strong interactions with theoretical and experimental highlights included. It is divided into five sections. The first section is devoted to the investigations into the QCD Vacuum and the latest results on the mechanism of quark confinement. The second and third sections focus respectively on light and heavy quarks (effective field theories, Schwinger-Dyson approach and lattice QCD results). The fourth section deals with the deconfinement mechanism and quark-gluon plasma formation signals. The last section presents highlights of experiments, new physics beyond QCD, and nonperturbative approaches in other theories (strings and SUSY) that may be useful in QCD.

This book presents the proceedings of a meeting intended to gather researchers working in the fields of harmonic analysis and global analysis to discuss some questions of common interest. About twenty talks covered the principal topics, illustrating the recent interactions between these two fields. The meeting started with a survey on spin geometry and was followed by talks on the spectrum of the Dirac operator in hyperbolic, Kahlerian and pseudo-Riemannian geometry. Different aspects of representation theory were discussed: Schubert cells, unitary representations with reflection symmetry, gradient operators, and Poisson transformations. Another series of talks was devoted to the systematic use of representation theory in global analysis; in particular on the Bernstein-Gelfand-Gelfand sequences in parabolic geometry, the construction of conformally covariant operators, and some refinements of the Kato inequality in Riemannian geometry. Various presentations ranging from general relativity to harmonic maps, by way of $4$-dimensional geometry/topology, Seiberg-Witten theory and the index theorem in $2$-dimensional hyperbolic geometry illustrated the diversity of applications of techniques from harmonic analysis.