Two algebraic byways from differential equations : Gröbner Bases and Quivers - Archive ouverte HAL Access content directly
Books Year : 2019

Two algebraic byways from differential equations : Gröbner Bases and Quivers

Kenji Iohara
  • Function : Author
  • PersonId : 905498
Philippe Malbos
Masa-Hiko Saito
  • Function : Author
  • PersonId : 885136
Nobuki Takayama
  • Function : Author
  • PersonId : 1044925

Abstract

This book presents a series of lectures focusing on differential equations from viewpoints of formal calculus and geometry through applications of quiver theory. Most of these lectures were given at the Kobe – Lyon Summer School in Mathematics on the theme On Quivers: Computational aspects and Geometric applications. This book consists of two parts. The first part introduces the theory of Gröbner bases in its commutative and noncommutative contexts. In particular, the lectures 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. The second part constitutes an introduction to representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line. All the contributions are presented without assuming any particular background and the authors have done their best to make the chapters suitable for graduate students.
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Dates and versions

hal-02084961 , version 1 (30-03-2019)

Identifiers

  • HAL Id : hal-02084961 , version 1

Cite

Kenji Iohara, Philippe Malbos, Masa-Hiko Saito, Nobuki Takayama. Two algebraic byways from differential equations : Gröbner Bases and Quivers. Springer, 28, inPress, Algorithms and Computations in Mathematics, 978-3-030-26453-6. ⟨hal-02084961⟩
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