Download or read book D modules and Microlocal Calculus written by Masaki Kashiwara and published by American Mathematical Soc.. This book was released on 2003 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book D Modules and Microlocal Geometry written by Masaki Kashiwara and published by Walter de Gruyter. This book was released on 2011-06-15 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Analytic D Modules and Applications written by Jan-Erik Björk and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic D modules written by Armand Borel and published by . This book was released on 1987 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presented here are recent developments in the algebraic theory of D-modules. The book contains an exposition of the basic notions and operations of D-modules, of special features of coherent, holonomic, and regular holonomic D-modules, and of the Riemann-Hilbert correspondence. The theory of Algebraic D-modules has found remarkable applications outside of analysis proper, in particular to infinite dimensional representations of semisimple Lie groups, to representations of Weyl groups, and to algebraic geometry.
Download or read book A Primer of Algebraic D Modules written by S. C. Coutinho and published by Cambridge University Press. This book was released on 1995-09-07 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book D Modules Perverse Sheaves and Representation Theory written by Kiyoshi Takeuchi and published by Springer Science & Business Media. This book was released on 2007-10-12 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.
Download or read book D Modules Perverse Sheaves and Representation Theory written by Ryoshi Hotta and published by Springer Science & Business Media. This book was released on 2007-11-07 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.
Download or read book Mixed Twistor D modules written by Takuro Mochizuki and published by Springer. This book was released on 2015-08-19 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce mixed twistor D-modules and establish their fundamental functorial properties. We also prove that they can be described as the gluing of admissible variations of mixed twistor structures. In a sense, mixed twistor D-modules can be regarded as a twistor version of M. Saito's mixed Hodge modules. Alternatively, they can be viewed as a mixed version of the pure twistor D-modules studied by C. Sabbah and the author. The theory of mixed twistor D-modules is one of the ultimate goals in the study suggested by Simpson's Meta Theorem and it would form a foundation for the Hodge theory of holonomic D-modules which are not necessarily regular singular.
Download or read book D modules Representation Theory and Quantum Groups written by Louis Boutet de Monvel and published by Springer. This book was released on 2006-11-15 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fundamentals of Algebraic Microlocal Analysis written by Goro Kato and published by CRC Press. This book was released on 2020-08-11 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."
Download or read book Regular and Irregular Holonomic D modules written by Masaki Kashiwara and published by . This book was released on 2016 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic and Analytic Microlocal Analysis written by Michael Hitrik and published by Springer. This book was released on 2018-12-19 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions from two workshops in algebraic and analytic microlocal analysis that took place in 2012 and 2013 at Northwestern University. Featured papers expand on mini-courses and talks ranging from foundational material to advanced research-level papers, and new applications in symplectic geometry, mathematical physics, partial differential equations, and complex analysis are discussed in detail. Topics include Procesi bundles and symplectic reflection algebras, microlocal condition for non-displaceability, polarized complex manifolds, nodal sets of Laplace eigenfunctions, geodesics in the space of Kӓhler metrics, and partial Bergman kernels. This volume is a valuable resource for graduate students and researchers in mathematics interested in understanding microlocal analysis and learning about recent research in the area.
Download or read book New Spaces in Mathematics written by Mathieu Anel and published by Cambridge University Press. This book was released on 2021-04 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this graduate-level book, leading researchers explore various new notions of 'space' in mathematics.
Download or read book Algebraic Theory of Differential Equations written by and published by Cambridge University Press. This book was released on with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sage for Undergraduates written by Gregory V. Bard and published by American Mathematical Society. This book was released on 2022-09-26 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the open-source and free alternative to expensive software like Maple™, Mathematica®, and MATLAB®, Sage offers anyone with a web browser the ability to use cutting-edge mathematical software and share the results with others, often with stunning graphics. This book is a gentle introduction to Sage for undergraduate students during Calculus II, Multivariate Calculus, Differential Equations, Linear Algebra, Math Modeling, or Operations Research. This book assumes no background in programming, but the reader who finishes the book will have learned about 60 percent of a first semester computer science course, including much of the Python programming language. The audience is not only math majors, but also physics, engineering, environmental science, finance, chemistry, economics, data science, and computer science majors. Many of the book's examples are drawn from those fields. Filled with “challenges” for the students to test their progress, the book is also ideal for self-study. What's New in the Second Edition: In 2019, Sage transitioned from Python 2 to Python 3, which changed the syntax in several significant ways, including for the print command. All the examples in this book have been rewritten to be compatible with Python 3. Moreover, every code block longer than four lines has been placed in an archive on the book's website http://www.sage-for-undergraduates.org that is maintained by the author, so that the students won't have to retype the code! Other additions include… The number of “challenges” for the students to test their own progress in learning Sage has roughly doubled, which will be a great boon for self-study.There's approximately 150 pages of new content, including: New projects on Leontief Input-Output Analysis and on Environmental ScienceNew sections on Complex Numbers and Complex Analysis, on SageTex, and on solving problems via Monte-Carlo Simulations.The first three sections of Chapter 1 have been completely rewritten to give absolute beginners a smoother transition into Sage.
Download or read book Twenty Four Hours of Local Cohomology written by Srikanth B. Iyengar and published by American Mathematical Society. This book was released on 2022-07-19 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Gröbner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.
Download or read book De Rham Cohomology of Differential Modules on Algebraic Varieties written by Yves André and published by Springer Nature. This book was released on 2020-07-16 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: "...A nice feature of the book [is] that at various points the authors provide examples, or rather counterexamples, that clearly show what can go wrong...This is a nicely-written book [that] studies algebraic differential modules in several variables." --Mathematical Reviews
