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Author : Masaki Kashiwara,Pierre Schapira
Publisher : Cambridge University Press
Page : 119 pages
File Size : 45,8 Mb
Release : 2016-05-26
Category : Mathematics
ISBN : 9781316613450
A unified treatment of the Riemann-Hilbert correspondence for (not necessarily regular) holonomic D-modules using indsheaves.
Author : D?ng Tr ng L
Publisher : World Scientific
Page : 320 pages
File Size : 53,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814273237
Mixing elementary results and advanced methods, Algebraic Approach to Differential Equations aims to accustom differential equation specialists to algebraic methods in this area of interest. It presents material from a school organized by The Abdus Salam International Centre for Theoretical Physics (ICTP), the Bibliotheca Alexandrina, and the International Centre for Pure and Applied Mathematics (CIMPA).
Author : Hedwig Heizinger
Publisher : Logos Verlag Berlin GmbH
Page : 70 pages
File Size : 52,8 Mb
Release : 2015-08-10
Category : D-modules
ISBN : 9783832540616
In this thesis we develop a way of examining the Stokes structure of certain irregular singular D-modules, namely the direct image of exponentially twisted meromorphic connections with regular singularities, in a topological point of view. We use this topological description to compute linear Stokes data for an explicit example.
Author : Armand Borel
Publisher : Unknown
Page : 382 pages
File Size : 45,7 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:49015000393570
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.
Author : Michael Hitrik,Dmitry Tamarkin,Boris Tsygan,Steve Zelditch
Publisher : Springer
Page : 654 pages
File Size : 55,7 Mb
Release : 2018-12-19
Category : Mathematics
ISBN : 9783030015886
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.
Author : Takuro Mochizuki
Publisher : Springer
Page : 487 pages
File Size : 46,6 Mb
Release : 2015-08-19
Category : Mathematics
ISBN : 9783319100883
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.
Author : Ashish K. Srivastava,Askar Tuganbaev,Pedro A. Guil Asensio
Publisher : Cambridge University Press
Page : 235 pages
File Size : 54,5 Mb
Release : 2021-03-18
Category : Mathematics
ISBN : 9781108949538
Provides a unified treatment of the study of modules invariant under automorphisms of their envelopes and covers.
Author : Jan-Erik Björk
Publisher : Springer Science & Business Media
Page : 588 pages
File Size : 45,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401707176
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 : Felipe Cano
Publisher : Springer Nature
Page : 500 pages
File Size : 41,5 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9783031541728
Author : Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo
Publisher : World Scientific
Page : 5396 pages
File Size : 52,5 Mb
Release : 2019-02-27
Category : Mathematics
ISBN : 9789813272897
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Author : Felix Fischer,Robert Johnson
Publisher : Cambridge University Press
Page : 305 pages
File Size : 44,6 Mb
Release : 2024-06-13
Category : Mathematics
ISBN : 9781009490535
This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.
Author : Aurelian Gheondea
Publisher : Cambridge University Press
Page : 128 pages
File Size : 55,6 Mb
Release : 2022-07-28
Category : Mathematics
ISBN : 9781108981279
This modern introduction to operator theory on spaces with indefinite inner product discusses the geometry and the spectral theory of linear operators on these spaces, the deep interplay with complex analysis, and applications to interpolation problems. The text covers the key results from the last four decades in a readable way with full proofs provided throughout. Step by step, the reader is guided through the intricate geometry and topology of spaces with indefinite inner product, before progressing to a presentation of the geometry and spectral theory on these spaces. The author carefully highlights where difficulties arise and what tools are available to overcome them. With generous background material included in the appendices, this text is an excellent resource for researchers in operator theory, functional analysis, and related areas as well as for graduate students.
Author : Kelli Francis-Staite,Dominic Joyce
Publisher : Cambridge University Press
Page : 224 pages
File Size : 48,7 Mb
Release : 2023-12-31
Category : Mathematics
ISBN : 9781009400206
Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C∞-schemes', which allow differential geometers to study a huge range of singular spaces, including 'infinitesimals' and infinite-dimensional spaces. These are applied in synthetic differential geometry, and derived differential geometry, the study of 'derived manifolds'. Differential geometers also study manifolds with corners. The cube is a 3-dimensional manifold with corners, with boundary the six square faces. This book introduces 'C∞-schemes with corners', singular spaces in differential geometry with good notions of boundary and corners. They can be used to define 'derived manifolds with corners' and 'derived orbifolds with corners'. These have applications to major areas of symplectic geometry involving moduli spaces of J-holomorphic curves. This work will be a welcome source of information and inspiration for graduate students and researchers working in differential or algebraic geometry.
Author : Caterina Campagnolo,Francesco Fournier-Facio,Nicolaus Heuer,Marco Moraschini
Publisher : Cambridge University Press
Page : 171 pages
File Size : 51,8 Mb
Release : 2022-11-30
Category : Mathematics
ISBN : 9781009183291
An overview of bounded cohomology and simplicial volume covering the basics of the subject and recent research directions.
Author : Alexander A. Ivanov
Publisher : Cambridge University Press
Page : 584 pages
File Size : 55,7 Mb
Release : 2023-08-17
Category : Mathematics
ISBN : 9781009338059
Covering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.
