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Algorithms and Computation in Mathematics
cover

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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eBook 51,16 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • Due: January 14, 2020
  • ISBN 978-3-030-26454-3
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover 88,39 €
price for Spain (gross)
  • Due: January 14, 2020
  • ISBN 978-3-030-26453-6
  • Free shipping for individuals worldwide
  • The final prices may differ from the prices shown due to specifics of VAT rules
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 20th 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 co-authored “Representation Theory of the Virasoro Algebra” (978-0-85729-159-2), 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.

Masa-Hiko 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, D-modules, and algebraic statistics. He co-authored “Gröbner Deformations of Hypergeometric Differential Equations” (978-3-540-66065-1), published by Springer.

Buy this book

eBook 51,16 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • Due: January 14, 2020
  • ISBN 978-3-030-26454-3
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover 88,39 €
price for Spain (gross)
  • Due: January 14, 2020
  • ISBN 978-3-030-26453-6
  • Free shipping for individuals worldwide
  • The final prices may differ from the prices shown due to specifics of VAT rules
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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
  • Masa-Hiko 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
978-3-030-26454-3
DOI
10.1007/978-3-030-26454-3
Hardcover ISBN
978-3-030-26453-6
Series ISSN
1431-1550
Edition Number
1
Number of Pages
X, 286
Number of Illustrations
12 b/w illustrations
Topics