Global Analysis And Harmonic Analysis

Global Analysis and Harmonic Analysis

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.

Handbook of Global Analysis

This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents

National Science Foundation