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, Kählerian 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.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians.