D-Modules and Microlocal Geometry PDF Download
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Author: Masaki Kashiwara
Publisher: Walter de Gruyter
ISBN: 3110856034
Category : Mathematics
Languages : en
Pages : 213
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Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author: Masaki Kashiwara
Publisher: Walter de Gruyter
ISBN: 3110856034
Category : Mathematics
Languages : en
Pages : 213
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Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author: Masaki Kashiwara
Publisher: American Mathematical Soc.
ISBN: 9780821827666
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Masaki Kashiwara is undoubtedly one of the masters of the theory of $D$-modules, and he has created a good, accessible entry point to the subject. The theory of $D$-modules is a very powerful point of view, bringing ideas from algebra and algebraic geometry to the analysis of systems of differential equations. It is often used in conjunction with microlocal analysis, as some of the important theorems are best stated or proved using these techniques. The theory has been used very successfully in applications to representation theory. Here, there is an emphasis on $b$-functions. These show up in various contexts: number theory, analysis, representation theory, and the geometry and invariants of prehomogeneous vector spaces. Some of the most important results on $b$-functions were obtained by Kashiwara. A hot topic from the mid '70s to mid '80s, it has now moved a bit more into the mainstream. Graduate students and research mathematicians will find that working on the subject in the two-decade interval has given Kashiwara a very good perspective for presenting the topic to the general mathematical public.
Author: S. C. Coutinho
Publisher: Cambridge University Press
ISBN: 0521551196
Category : Mathematics
Languages : en
Pages : 223
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Book Description
The theory of D-modules is a rich area of study combining ideas from algebra and differential equations, and it has significant applications to diverse areas such as singularity theory and representation theory. This book introduces D-modules and their applications avoiding all unnecessary over-sophistication. It is aimed at beginning graduate students and the approach taken is algebraic, concentrating on the role of the Weyl algebra. Very few prerequisites are assumed, and the book is virtually self-contained. Exercises are included at the end of each chapter and the reader is given ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area.
Author: Louis Boutet de Monvel
Publisher: Springer
ISBN: 3540481958
Category : Mathematics
Languages : en
Pages : 226
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Book Description
CONTENTS: L. Boutet de Monvel: Indice de systemes differentiels.- C. De Concini, C. Procesi: Quantum groups.- P. Schapira, J.P. Schneiders: Index theorems for R-constructible sheaves and for D-modules.- N. Berline, M. Vergne: The equivariant Chern character and index of G-invariant operators.
Author: Maciej Zworski
Publisher: American Mathematical Soc.
ISBN: 0821883208
Category : Mathematics
Languages : en
Pages : 448
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Book Description
"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.
Author: Goro Kato
Publisher: CRC Press
ISBN: 1000148394
Category : Mathematics
Languages : en
Pages : 320
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Book Description
"Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analytic and algebraic aspects."
Author: Jan-Erik Björk
Publisher: Springer Science & Business Media
ISBN: 9401707170
Category : Mathematics
Languages : en
Pages : 588
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Book Description
This is the first monograph to be published on analytic D-modules and it offers a complete and systematic treatment of the foundations together with a thorough discussion of such modern topics as the Riemann--Hilbert correspondence, Bernstein--Sata polynomials and a large variety of results concerning microdifferential analysis. Analytic D-module theory studies holomorphic differential systems on complex manifolds. It brings new insight and methods into many areas, such as infinite dimensional representations of Lie groups, asymptotic expansions of hypergeometric functions, intersection cohomology on Kahler manifolds and the calculus of residues in several complex variables. The book contains seven chapters and has an extensive appendix which is devoted to the most important tools which are used in D-module theory. This includes an account of sheaf theory in the context of derived categories, a detailed study of filtered non-commutative rings and homological algebra, and the basic material in symplectic geometry and stratifications on complex analytic sets. For graduate students and researchers.
Author: Masaki Kashiwara
Publisher: Springer Science & Business Media
ISBN: 3662026619
Category : Mathematics
Languages : en
Pages : 522
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Book Description
Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.
Author: Mircea Mustaţă
Publisher: American Mathematical Soc.
ISBN: 1470437813
Category : Education
Languages : en
Pages : 92
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Book Description
The authors use methods from birational geometry to study the Hodge filtration on the localization along a hypersurface. This filtration leads to a sequence of ideal sheaves, called Hodge ideals, the first of which is a multiplier ideal. They analyze their local and global properties, and use them for applications related to the singularities and Hodge theory of hypersurfaces and their complements.
Author: Alan Adolphson
Publisher: Walter de Gruyter
ISBN: 3110198134
Category : Mathematics
Languages : en
Pages : 1150
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Book Description
This two-volume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923 - 1998). It presents a wide-ranging overview of some of the most active areas of contemporary research in arithmetic algebraic geometry, with special emphasis on the geometric applications of the p-adic analytic techniques originating in Dwork's work, their connection to various recent cohomology theories and to modular forms. The two volumes contain both important new research and illuminating survey articles written by leading experts in the field. The book will provide an indispensable resource for all those wishing to approach the frontiers of research in arithmetic algebraic geometry.
