Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers
Editors: Iohara, K., Malbos, P., Saito, M.H., Takayama, N. (Eds.)
 Presents Gröbner bases and quiver theories as providers of computing models for differential equations and systems
 Offers a historical background for a better understanding of how theories developed
 Appeals to a wide readership, from graduate students to researchers and scholars
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 About this book

This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types. Although the theory of Gröbner bases was developed in the second half of the 20^{th} century, many works on computational methods in algebra were published well before the introduction of the modern algebraic language. Since then, new algorithms have been developed and the theory itself has greatly expanded. In comparison, diagrammatic methods in representation theory are relatively new, with the quiver varieties only being introduced – with big impact – in the 1990s.
Divided into two parts, the book first discusses the theory of Gröbner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Gröbner bases to analysis on systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. It then introduces representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line.
While no particular reader background is assumed, the book is intended for graduate students in mathematics, engineering and related fields, as well as researchers and scholars.
 About the authors

Kenji Iohara is a Professor at Université Claude Bernard Lyon 1, France. His research focuses mainly on the Lie theory, singularity, and special functions. He coauthored “Representation Theory of the Virasoro Algebra” (9780857291592), published with Springer.
Philippe Malbos is a Professor at Université Claude Bernard Lyon 1, France. His fields of research include algebraic rewriting, Gröbner bases, and homological algebra.
MasaHiko Saito is a Professor and Director of the Center for Mathematical and Data Sciences at Kobe University, Japan. His interests include algebraic geometry and its applications to integrable systems.
Nobuki Takayama is a Professor at Kobe University, Japan. His research fields comprise computer algebra, hypergeometric functions, Dmodules, and algebraic statistics. He coauthored “Gröbner Deformations of Hypergeometric Differential Equations” (9783540660651), published by Springer.
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Bibliographic Information
 Bibliographic Information

 Book Title
 Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers
 Editors

 Kenji Iohara
 Philippe Malbos
 MasaHiko Saito
 Nobuki Takayama
 Series Title
 Algorithms and Computation in Mathematics
 Series Volume
 28
 Copyright
 2019
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer Nature Switzerland AG
 eBook ISBN
 9783030264543
 DOI
 10.1007/9783030264543
 Hardcover ISBN
 9783030264536
 Series ISSN
 14311550
 Edition Number
 1
 Number of Pages
 X, 286
 Number of Illustrations
 12 b/w illustrations
 Topics