Jacques Sauloy's Books

Differential Galois Theory through Riemann-Hilbert Correspondence

By: Jacques Sauloy

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Differential Galois Theory through Riemann-Hilbert Correspondence

By: Jacques Sauloy

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.

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303

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American Mathematical Soc.

Published Date

ISBN 10

1470430959

ISBN 13

9781470430955

Galois Theories of Linear Difference Equations: An Introduction

By: Charlotte Hardouin,Jacques Sauloy,Michael F. Singer

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Galois Theories of Linear Difference Equations: An Introduction

By: Charlotte Hardouin,Jacques Sauloy,Michael F. Singer

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.

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Page Count

185

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470426552

ISBN 13

9781470426552

Differential Galois Theory through Riemann-Hilbert Correspondence

By: Jacques Sauloy

Write a review Read reviews Take a Quiz Solve Book Puzzle

Differential Galois Theory through Riemann-Hilbert Correspondence

By: Jacques Sauloy

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

303

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470430959

ISBN 13

9781470430955

Book's by Jacques Sauloy

Differential Galois Theory through Riemann-Hilbert Correspondence

Differential Galois Theory through Riemann-Hilbert Correspondence

Galois Theories of Linear Difference Equations: An Introduction

Galois Theories of Linear Difference Equations: An Introduction

Differential Galois Theory through Riemann-Hilbert Correspondence

Differential Galois Theory through Riemann-Hilbert Correspondence

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