[PDF] Galois Theories Of Linear Difference Equations An Introduction eBook

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Galois Theories of Linear Difference Equations: An Introduction

Charlotte Hardouin
Galois Theories of Linear Difference Equations: An Introduction by Charlotte Hardouin PDF

Author : Charlotte Hardouin
Publisher : American Mathematical Soc.
Page : 185 pages
File Size : 27,98 MB
Release : 2016-04-27
Category : Mathematics
ISBN : 1470426552

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This book is a collection of three introductory tutorials coming out of three courses given at the CIMPA Research School “Galois Theory of Difference Equations” in Santa Marta, Columbia, July 23–August 1, 2012. The aim of these tutorials is to introduce the reader to three Galois theories of linear difference equations and their interrelations. Each of the three articles addresses a different galoisian aspect of linear difference equations. The authors motivate and give elementary examples of the basic ideas and techniques, providing the reader with an entry to current research. In addition each article contains an extensive bibliography that includes recent papers; the authors have provided pointers to these articles allowing the interested reader to explore further.

Galois Theory of Linear Differential Equations

Marius van der Put
Galois Theory of Linear Differential Equations by Marius van der Put PDF

Author : Marius van der Put
Publisher : Springer Science & Business Media
Page : 446 pages
File Size : 25,35 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642557503

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From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews

Differential Galois Theory through Riemann-Hilbert Correspondence

Jacques Sauloy
Differential Galois Theory through Riemann-Hilbert Correspondence by Jacques Sauloy PDF

Author : Jacques Sauloy
Publisher : American Mathematical Soc.
Page : 303 pages
File Size : 17,47 MB
Release : 2016-12-07
Category : Mathematics
ISBN : 1470430959

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Differential Galois theory is an important, fast developing area which appears more and more in graduate courses since it mixes fundamental objects from many different areas of mathematics in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot Theory, was purely algebraic. This approach has been extensively developed and is well covered in the literature. An alternative approach consists in tagging algebraic objects with transcendental information which enriches the understanding and brings not only new points of view but also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot approach is not easily extended. This book offers a hands-on transcendental approach to differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it provides a smooth, down-to-earth introduction to algebraic geometry, category theory and tannakian duality. Since the book studies only complex analytic linear differential equations, the main prerequisites are complex function theory, linear algebra, and an elementary knowledge of groups and of polynomials in many variables. A large variety of examples, exercises, and theoretical constructions, often via explicit computations, offers first-year graduate students an accessible entry into this exciting area.

Lectures on Differential Galois Theory

Andy R. Magid
Lectures on Differential Galois Theory by Andy R. Magid PDF

Author : Andy R. Magid
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 19,15 MB
Release :
Category : Mathematics
ISBN : 9780821882665

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Providing a self-contained development with many explicit examples, this book is a unique approach to Galois theory and is suitable as a textbook at the advanced graduate level.

Symmetries and Integrability of Difference Equations

Decio Levi
Symmetries and Integrability of Difference Equations by Decio Levi PDF

Author : Decio Levi
Publisher : Springer
Page : 441 pages
File Size : 25,89 MB
Release : 2017-06-30
Category : Science
ISBN : 3319566660

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This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers.

Arithmetic and Geometry over Local Fields

Bruno Anglès
Arithmetic and Geometry over Local Fields by Bruno Anglès PDF

Author : Bruno Anglès
Publisher : Springer Nature
Page : 337 pages
File Size : 11,9 MB
Release : 2021-03-03
Category : Mathematics
ISBN : 3030662497

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This volume introduces some recent developments in Arithmetic Geometry over local fields. Its seven chapters are centered around two common themes: the study of Drinfeld modules and non-Archimedean analytic geometry. The notes grew out of lectures held during the research program "Arithmetic and geometry of local and global fields" which took place at the Vietnam Institute of Advanced Study in Mathematics (VIASM) from June to August 2018. The authors, leading experts in the field, have put great effort into making the text as self-contained as possible, introducing the basic tools of the subject. The numerous concrete examples and suggested research problems will enable graduate students and young researchers to quickly reach the frontiers of this fascinating branch of mathematics.