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Singularity theory encompasses many different aspects of geometry and topology, and an overview of these is represented here by papers given at the International Singularity Conference held in 1991 at Lille. The conference attracted researchers from a wide variety of subject areas, including differential and algebraic geometry, topology, and mathematical physics. Some of the best known figures in their fields participated, and their papers have been collected here. Contributors to this volume include G. Barthel, J. W. Bruce, F. Delgado, M. Ferrarotti, G. M. Greuel, J. P. Henry, L. Kaup, B. Lichtin, B. Malgrange, M. Merle, D. Mond, L. Narvaez, V. Neto, A. A. Du Plessis, R. Thom and M. Vaquié. Research workers in singularity theory or related subjects will find that this book contains a wealth of valuable information on all aspects of the subject.
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This short introduction to microlocal analysis is presented, in the spirit of Hörmander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjöstrand emphasise the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions. The contents of the book correspond to a graduate course given many times by the authors. It should prove to be useful to mathematicians and theoretical physicists, either to enrich their general knowledge of this area, or as preparation for the current research literature.
Differential operators. --- Microlocal analysis. --- Functional analysis --- Operators, Differential --- Differential equations --- Operator theory --- Pseudodifferential operators --- Opérateurs pseudo-différentiels --- Singularities (Mathematics) --- Singularités (mathématiques) --- Analyse microlocale --- Fourier, Opérateurs intégraux de
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Algebraic topology --- Hodge theory --- Jordan matrix --- Singularities (Mathematics) --- Hodge, Théorie de --- Singularités (mathématiques) --- Geometry, Algebraic --- Form, Jordan --- Form, Jordan normal --- Jordan form --- Jordan normal form --- Matrix, Jordan --- Matrices --- Complex manifolds --- Differentiable manifolds --- Homology theory --- Hodge, Théorie de.
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Ordered algebraic structures --- Cohen-Macaulay rings --- Gorenstein rings --- Homology theory --- Singularities (Mathematics) --- Geometry, Algebraic --- Cohomology theory --- Contrahomology theory --- Algebraic topology --- Gorenstein's rings --- Rings, Gorenstein --- Noetherian rings --- Macaulay local rings --- Macaulay rings, Cohen --- -Rings, Cohen-Macaulay --- Rings, Macaulay local --- Local rings --- Singularités (mathématiques) --- Homologie --- Anneaux de Gorenstein --- Cohen-Macaulay, Anneaux de --- Homologie. --- Anneaux de Gorenstein. --- Cohen-Macaulay, Anneaux de.
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Differential equations, Nonlinear --- Mathematical physics --- Singularities (Mathematics) --- Superconductors --- Superfluidity --- Equations différentielles non linéaires --- Physique mathématique --- Singularités (Mathématiques) --- Numerical solutions --- Mathematics --- Solutions numériques --- Mathematics. --- Numerical solutions. --- Equations différentielles non linéaires --- Physique mathématique --- Singularités (Mathématiques) --- Solutions numériques --- Superconductors - Mathematics. --- Superfluidity - Mathematics. --- Differential equations, Nonlinear - Numerical solutions.
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