Author : Masaki Kashiwara
Publisher : Cambridge University Press
Page : 119 pages
File Size : 36,25 MB
Release : 2016-05-26
Category : Mathematics
ISBN : 1316613453
A unified treatment of the Riemann-Hilbert correspondence for (not necessarily regular) holonomic D-modules using indsheaves.
Author : Masaki Kashiwara
Publisher :
Page : 111 pages
File Size : 23,71 MB
Release : 2016
Category : D-modules
ISBN : 9781316675625
Author : Jan-Erik Björk
Publisher : Springer Science & Business Media
Page : 588 pages
File Size : 25,42 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 9401707170
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 : Scott Balchin
Publisher : Cambridge University Press
Page : 357 pages
File Size : 50,90 MB
Release : 2021-11-18
Category : Mathematics
ISBN : 1108931944
A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.
Author : Pieter Belmans
Publisher : Cambridge University Press
Page : 307 pages
File Size : 19,38 MB
Release : 2022-10-31
Category : Mathematics
ISBN : 1009054856
A collection of expository articles on modern topics in algebraic geometry, focusing on the geometry of algebraic spaces and stacks.
Author : Jan-Hendrik Evertse
Publisher : Cambridge University Press
Page : 242 pages
File Size : 25,76 MB
Release : 2022-04-28
Category : Mathematics
ISBN : 1009050036
This book provides the first thorough treatment of effective results and methods for Diophantine equations over finitely generated domains. Compiling diverse results and techniques from papers written in recent decades, the text includes an in-depth analysis of classical equations including unit equations, Thue equations, hyper- and superelliptic equations, the Catalan equation, discriminant equations and decomposable form equations. The majority of results are proved in a quantitative form, giving effective bounds on the sizes of the solutions. The necessary techniques from Diophantine approximation and commutative algebra are all explained in detail without requiring any specialized knowledge on the topic, enabling readers from beginning graduate students to experts to prove effective finiteness results for various further classes of Diophantine equations.
Author : Paolo Aluffi
Publisher : Cambridge University Press
Page : 395 pages
File Size : 33,36 MB
Release : 2022-04-07
Category : Mathematics
ISBN : 1108792510
Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.
Author : Jeffrey Shallit
Publisher : Cambridge University Press
Page : 376 pages
File Size : 18,13 MB
Release : 2022-09-30
Category : Computers
ISBN : 1108786979
Automatic sequences are sequences over a finite alphabet generated by a finite-state machine. This book presents a novel viewpoint on automatic sequences, and more generally on combinatorics on words, by introducing a decision method through which many new results in combinatorics and number theory can be automatically proved or disproved with little or no human intervention. This approach to proving theorems is extremely powerful, allowing long and error-prone case-based arguments to be replaced by simple computations. Readers will learn how to phrase their desired results in first-order logic, using free software to automate the computation process. Results that normally require multipage proofs can emerge in milliseconds, allowing users to engage with mathematical questions that would otherwise be difficult to solve. With more than 150 exercises included, this text is an ideal resource for researchers, graduate students, and advanced undergraduates studying combinatorics, sequences, and number theory.
Author : Vladimir Dotsenko
Publisher : Cambridge University Press
Page : 188 pages
File Size : 18,55 MB
Release : 2023-08-31
Category : Mathematics
ISBN : 1108967027
Covering an exceptional range of topics, this text provides a unique overview of the Maurer—Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.
Author : Anthony Nixon
Publisher : Cambridge University Press
Page : 258 pages
File Size : 34,8 MB
Release : 2022-06-09
Category : Mathematics
ISBN : 1009115464
This volume contains eight survey articles by the invited speakers of the 29th British Combinatorial Conference, held at Lancaster University in July 2022. Each article provides an overview of recent developments in a current hot research topic in combinatorics. These topics span graphs and hypergraphs, Latin squares, linear programming, finite fields, extremal combinatorics, Ramsey theory, graph minors and tropical geometry. The authors are among the world's foremost researchers on their respective topics but their surveys are aimed at nonspecialist readers: they are written clearly with little prior knowledge assumed and with pointers to the wider literature. Taken together these surveys give a snapshot of the research frontier in contemporary combinatorics, making the latest developments accessible to researchers and graduate students in mathematics and theoretical computer science with an interest in combinatorics and helping them to keep abreast of the field.
