Analytic D Modules And Applications

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Analytic D-Modules and Applications

Jan-Erik Björk
Analytic D Modules and Applications Book PDF

Author : Jan-Erik Björk
Publisher : Springer Science & Business Media
Page : 588 pages
File Size : 47,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401707176

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Analytic D-Modules and Applications by Jan-Erik Björk Pdf

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.

The Heart of Cohomology

Goro Kato
The Heart of Cohomology Book PDF

Author : Goro Kato
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 44,8 Mb
Release : 2006-11-08
Category : Mathematics
ISBN : 9781402050367

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The Heart of Cohomology by Goro Kato Pdf

If you have not heard about cohomology, The Heart of Cohomology may be suited for you. The book gives Fundamental notions in cohomology for examples, functors, representable functors, Yoneda embedding, derived functors, spectral sequences, derived categories are explained in elementary fashion. Applications to sheaf cohomology. In addition, the book examines cohomological aspects of D-modules and of the computation of zeta functions of the Weierstrass family.

Mixed Twistor D-modules

Takuro Mochizuki
Mixed Twistor D modules Book PDF

Author : Takuro Mochizuki
Publisher : Springer
Page : 487 pages
File Size : 44,6 Mb
Release : 2015-08-19
Category : Mathematics
ISBN : 9783319100883

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Mixed Twistor D-modules by Takuro Mochizuki Pdf

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.

Equivariant Analytic Localization of Group Representations

Laura Ann Smithies
Equivariant Analytic Localization of Group Representations Book PDF

Author : Laura Ann Smithies
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 46,9 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821827253

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Equivariant Analytic Localization of Group Representations by Laura Ann Smithies Pdf

The problem of producing geometric constructions of the linear representations of a real connected semisimple Lie group with finite center, $G_0$, has been of great interest to representation theorists for many years now. A classical construction of this type is the Borel-Weil theorem, which exhibits each finite dimensional irreducible representation of $G_0$ as the space of global sections of a certain line bundle on the flag variety $X$ of the complexified Lie algebra $\mathfrak g$ of $G_0$.In 1990, Henryk Hecht and Joseph Taylor introduced a technique called analytic localization which vastly generalized the Borel-Weil theorem. Their method is similar in spirit to Beilinson and Bernstein's algebraic localization method, but it applies to $G_0$ representations themselves, instead of to their underlying Harish-Chandra modules. For technical reasons, the equivalence of categories implied by the analytic localization method is not as strong as it could be. In this paper, a refinement of the Hecht-Taylor method, called equivariant analytic localization, is developed. The technical advantages that equivariant analytic localization has over (non-equivariant) analytic localization are discussed and applications are indicated.

D-Modules, Perverse Sheaves, and Representation Theory

Kiyoshi Takeuchi,Ryoshi Hotta,Toshiyuki Tanisaki
D Modules Perverse Sheaves and Representation Theory Book PDF

Author : Kiyoshi Takeuchi,Ryoshi Hotta,Toshiyuki Tanisaki
Publisher : Springer Science & Business Media
Page : 412 pages
File Size : 41,6 Mb
Release : 2007-10-12
Category : Mathematics
ISBN : 9780817645236

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D-Modules, Perverse Sheaves, and Representation Theory by Kiyoshi Takeuchi,Ryoshi Hotta,Toshiyuki Tanisaki Pdf

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.

Commutative Algebra

Luchezar L. Avramov,Marc Chardin,Marcel Morales,Claudia Polini
Commutative Algebra Book PDF

Author : Luchezar L. Avramov,Marc Chardin,Marcel Morales,Claudia Polini
Publisher : American Mathematical Soc.
Page : 376 pages
File Size : 41,5 Mb
Release : 2003
Category : Commutative algebra
ISBN : 9780821832332

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Commutative Algebra by Luchezar L. Avramov,Marc Chardin,Marcel Morales,Claudia Polini Pdf

This volume contains 21 articles based on invited talks given at two international conferences held in France in 2001. Most of the papers are devoted to various problems of commutative algebra and their relation to properties of algebraic varieties. The book is suitable for graduate students and research mathematicians interested in commutative algebra and algebraic geometry.

From Fourier Analysis and Number Theory to Radon Transforms and Geometry

Hershel M. Farkas,Robert C. Gunning,Marvin I. Knopp,B. A. Taylor
From Fourier Analysis and Number Theory to Radon Transforms and Geometry Book PDF

Author : Hershel M. Farkas,Robert C. Gunning,Marvin I. Knopp,B. A. Taylor
Publisher : Springer Science & Business Media
Page : 567 pages
File Size : 49,5 Mb
Release : 2012-09-18
Category : Mathematics
ISBN : 9781461440741

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From Fourier Analysis and Number Theory to Radon Transforms and Geometry by Hershel M. Farkas,Robert C. Gunning,Marvin I. Knopp,B. A. Taylor Pdf

​​​A memorial conference for Leon Ehrenpreis was held at Temple University, November 15-16, 2010. In the spirit of Ehrenpreis’s contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis and a bit of applied mathematics. With the exception of one survey article, the papers in this volume are all new results in the various fields in which Ehrenpreis worked . There are papers in pure analysis, papers in number theory, papers in what may be called applied mathematics such as population biology and parallel refractors and papers in partial differential equations. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore.​A biographical sketch of Leon Ehrenpreis by his daughter, a professional journalist, enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician.

Geometric Aspects of Dwork Theory

Alan Adolphson,Francesco Baldassarri,Pierre Berthelot,Nicholas Katz,Francois Loeser
Geometric Aspects of Dwork Theory Book PDF

Author : Alan Adolphson,Francesco Baldassarri,Pierre Berthelot,Nicholas Katz,Francois Loeser
Publisher : Walter de Gruyter
Page : 1150 pages
File Size : 43,6 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110198133

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Geometric Aspects of Dwork Theory by Alan Adolphson,Francesco Baldassarri,Pierre Berthelot,Nicholas Katz,Francois Loeser Pdf

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.

D-Modules, Perverse Sheaves, and Representation Theory

Ryoshi Hotta,Toshiyuki Tanisaki
D Modules Perverse Sheaves and Representation Theory Book PDF

Author : Ryoshi Hotta,Toshiyuki Tanisaki
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 48,9 Mb
Release : 2007-11-07
Category : Mathematics
ISBN : 9780817643638

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D-Modules, Perverse Sheaves, and Representation Theory by Ryoshi Hotta,Toshiyuki Tanisaki Pdf

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.

Quantitative Tamarkin Theory

Jun Zhang
Quantitative Tamarkin Theory Book PDF

Author : Jun Zhang
Publisher : Springer Nature
Page : 152 pages
File Size : 40,7 Mb
Release : 2020-03-09
Category : Mathematics
ISBN : 9783030378882

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Quantitative Tamarkin Theory by Jun Zhang Pdf

This textbook offers readers a self-contained introduction to quantitative Tamarkin category theory. Functioning as a viable alternative to the standard algebraic analysis method, the categorical approach explored in this book makes microlocal sheaf theory accessible to a wide audience of readers interested in symplectic geometry. Much of this material has, until now, been scattered throughout the existing literature; this text finally collects that information into one convenient volume. After providing an overview of symplectic geometry, ranging from its background to modern developments, the author reviews the preliminaries with precision. This refresher ensures readers are prepared for the thorough exploration of the Tamarkin category that follows. A variety of applications appear throughout, such as sheaf quantization, sheaf interleaving distance, and sheaf barcodes from projectors. An appendix offers additional perspectives by highlighting further useful topics. Quantitative Tamarkin Theory is ideal for graduate students interested in symplectic geometry who seek an accessible alternative to the algebraic analysis method. A background in algebra and differential geometry is recommended. This book is part of the "Virtual Series on Symplectic Geometry" http://www.springer.com/series/16019

Microlocal Analysis and Complex Fourier Analysis

Takahiro Kawai,Keiko Fujita
Microlocal Analysis and Complex Fourier Analysis Book PDF

Author : Takahiro Kawai,Keiko Fujita
Publisher : World Scientific
Page : 340 pages
File Size : 53,5 Mb
Release : 2002-12-12
Category : Mathematics
ISBN : 9789814487504

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Microlocal Analysis and Complex Fourier Analysis by Takahiro Kawai,Keiko Fujita Pdf

This book is a collection of original papers on microlocal analysis, Fourier analysis in the complex domain, generalized functions and related topics. Most of the papers originate from the talks given at the conference “Prospects of Generalized Functions” (in November, 2001 at RIMS, Kyoto). Reflecting the fact that the papers, except M Morimoto's one, are dedicated to Mitsuo Morimoto, the subjects considered in this book are interdisciplinary, just as Morimoto's works are. The historical backgrounds of the subjects are also discussed in depth in some contributions. Thus, this book should be valuable not only to the specialists in the fields, but also to those who are interested in the history of modern mathematics such as distributions and hyperfunctions. Contents:Vanishing of Stokes Curves (T Aoki et al.)Parabolic Equations with Singularity on the Boundary (C P Arceo et al.)Residues: Analysis or Algebra? (C A Berenstein)Heat Equation via Generalized Functions (S-Y Chung)Bergman Transformation for Analytic Functionals on Some Balls (K Fujita)On Infra-Red Singularities Associated with QC Photons (T Kawai & H P Stapp)Hyperfunctions and Kernel Method (D Kim)The Effect of New Stokes Curves in the Exact Steepest Descent Method (T Koike & Y Takei)Boehmians on the Sphere and Zonal Spherical Functions (M Morimoto)On a Generalization of the Laurent Expansion (Y Saburi)Domains of Convergence of Laplace Series (J Siciak)The Reproducing Kernels of the Space of Harmonic Polynomials in the Case of Real Rank 1 (R Wada & Y Agaoka)and other papers Readership: Graduate students in analysis or differential geometry and specialists in generalized functions, differential equations, analytic functions and complex WKB analysis. Keywords:

Regular and Irregular Holonomic D-Modules

Masaki Kashiwara,Pierre Schapira
Regular and Irregular Holonomic D Modules Book PDF

Author : Masaki Kashiwara,Pierre Schapira
Publisher : Cambridge University Press
Page : 119 pages
File Size : 47,8 Mb
Release : 2016-05-26
Category : Mathematics
ISBN : 9781316613450

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Regular and Irregular Holonomic D-Modules by Masaki Kashiwara,Pierre Schapira Pdf

A unified treatment of the Riemann-Hilbert correspondence for (not necessarily regular) holonomic D-modules using indsheaves.

Gröbner Bases in Symbolic Analysis

Markus Rosenkranz,Dongming Wang
Gr bner Bases in Symbolic Analysis Book PDF

Author : Markus Rosenkranz,Dongming Wang
Publisher : Walter de Gruyter
Page : 361 pages
File Size : 40,6 Mb
Release : 2011-12-22
Category : Mathematics
ISBN : 9783110922752

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Gröbner Bases in Symbolic Analysis by Markus Rosenkranz,Dongming Wang Pdf

This volume contains survey articles and original research papers, presenting the state of the art on applying the symbolic approach of Gröbner bases and related methods to differential and difference equations. The contributions are based on talks delivered at the Special Semester on Gröbner Bases and Related Methods hosted by the Johann Radon Institute of Computational and Applied Mathematics, Linz, Austria, in May 2006.

An Introduction to Intersection Homology Theory, Second Edition

Frances Kirwan,Jonathan Woolf
An Introduction to Intersection Homology Theory Second Edition Book PDF

Author : Frances Kirwan,Jonathan Woolf
Publisher : CRC Press
Page : 250 pages
File Size : 53,9 Mb
Release : 2006-06-07
Category : Mathematics
ISBN : 1584881844

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An Introduction to Intersection Homology Theory, Second Edition by Frances Kirwan,Jonathan Woolf Pdf

Now more that a quarter of a century old, intersection homology theory has proven to be a powerful tool in the study of the topology of singular spaces, with deep links to many other areas of mathematics, including combinatorics, differential equations, group representations, and number theory. Like its predecessor, An Introduction to Intersection Homology Theory, Second Edition introduces the power and beauty of intersection homology, explaining the main ideas and omitting, or merely sketching, the difficult proofs. It treats both the basics of the subject and a wide range of applications, providing lucid overviews of highly technical areas that make the subject accessible and prepare readers for more advanced work in the area. This second edition contains entirely new chapters introducing the theory of Witt spaces, perverse sheaves, and the combinatorial intersection cohomology of fans. Intersection homology is a large and growing subject that touches on many aspects of topology, geometry, and algebra. With its clear explanations of the main ideas, this book builds the confidence needed to tackle more specialist, technical texts and provides a framework within which to place them.

Twenty-Four Hours of Local Cohomology

Srikanth B. Iyengar,Graham J. Leuschke,Anton Leykin,Claudia Miller,Ezra Miller,Anurag K. Singh,Uli Walther
Twenty Four Hours of Local Cohomology Book PDF

Author : Srikanth B. Iyengar,Graham J. Leuschke,Anton Leykin,Claudia Miller,Ezra Miller,Anurag K. Singh,Uli Walther
Publisher : American Mathematical Society
Page : 108 pages
File Size : 54,9 Mb
Release : 2022-07-19
Category : Mathematics
ISBN : 9781470471590

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Twenty-Four Hours of Local Cohomology by Srikanth B. Iyengar,Graham J. Leuschke,Anton Leykin,Claudia Miller,Ezra Miller,Anurag K. Singh,Uli Walther Pdf

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.