What do you think?
Rate this book
Differential Galois Theory Through Riemann-Hilbert Correspondence: An Elementary Introduction (Graduate Studies in Mathematics)
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.
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.
275 pages, Hardcover
First published March 30, 2017
2 people want to read
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 of 1 review
December 2, 2022
Outstandingly insightful and well written, both accessible and profound, Sauloy's approach to the Differential Galois Theory is much more down-to-earth than the classical one, and bypasses (where possible) the obscurities of advanced algebra that are the real gatekeepers of the more canonic monographs (Singer, Zoladek, Arnol'd, Magid), comprehensive and brilliant as they are.
This concrete point of view highly benefits a Theory that is well-developed but (at least apparently) in lack of examples, and shines an intriguing light on the modern tools from category and module theory and algebraic topology and geometry that are currently in use.
Not a handbook but a book, in fact the latest good book on Differential Galois Theory.
This concrete point of view highly benefits a Theory that is well-developed but (at least apparently) in lack of examples, and shines an intriguing light on the modern tools from category and module theory and algebraic topology and geometry that are currently in use.
Not a handbook but a book, in fact the latest good book on Differential Galois Theory.
Displaying 1 of 1 review