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Two algebraic byways from differenti...

Iohara, Kenji.

Two algebraic byways from differential equationsGrobner bases and quivers /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Two algebraic byways from differential equationsedited by Kenji Iohara ... [et al.].
Reminder of title:	Grobner bases and quivers /
other author:	Iohara, Kenji.
Published:	Cham :Springer International Publishing :2020.
Description:	xi, 371 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Grobner bases.
Online resource:	https://doi.org/10.1007/978-3-030-26454-3
ISBN:	9783030264543$q(electronic bk.)

Two algebraic byways from differential equationsGrobner bases and quivers /
Two algebraic byways from differential equationsGrobner bases and quivers /[electronic resource] :edited by Kenji Iohara ... [et al.]. - Cham :Springer International Publishing :2020. - xi, 371 p. :ill., digital ;24 cm. - Algorithms and computation in mathematics,v.281431-1550 ;. - Algorithms and computation in mathematics ;v.5..

Part I First Byway: Grobner Bases -- 1 From Analytical Mechanical Problems to Rewriting Theory Through M. Janet -- 2 Grobner Bases in D-modules: Application to Bernstein-Sato Polynomials -- 3 Introduction to Algorithms for D-Modules with Quiver D-Modules -- 4 Noncommutative Grobner Bases: Applications and Generalizations -- 5 Introduction to Computational Algebraic Statistics -- Part II Second Byway: Quivers -- 6 Introduction to Representations of Quivers -- 7 Introduction to Quiver Varieties -- 8 On Additive Deligne-Simpson Problems -- 9 Applications of Quiver Varieties to Moduli Spaces of Connections on P1.

This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Grobner bases) and geometry (via quiver theory) Grobner bases serve as effective models for computation in algebras of various types. Although the theory of Grobner 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 Grobner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Grobner 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.

ISBN: 9783030264543$q(electronic bk.)

Standard No.: 10.1007/978-3-030-26454-3doiSubjects--Topical Terms:

209325
Grobner bases.

LC Class. No.: QA251.3 / .T863 2020

Dewey Class. No.: 512.44

Two algebraic byways from differential equationsGrobner bases and quivers /
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505 0 $a Part I First Byway: Grobner Bases -- 1 From Analytical Mechanical Problems to Rewriting Theory Through M. Janet -- 2 Grobner Bases in D-modules: Application to Bernstein-Sato Polynomials -- 3 Introduction to Algorithms for D-Modules with Quiver D-Modules -- 4 Noncommutative Grobner Bases: Applications and Generalizations -- 5 Introduction to Computational Algebraic Statistics -- Part II Second Byway: Quivers -- 6 Introduction to Representations of Quivers -- 7 Introduction to Quiver Varieties -- 8 On Additive Deligne-Simpson Problems -- 9 Applications of Quiver Varieties to Moduli Spaces of Connections on P1.
520 $a This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Grobner bases) and geometry (via quiver theory) Grobner bases serve as effective models for computation in algebras of various types. Although the theory of Grobner 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 Grobner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Grobner 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.
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650 2 4 $a Associative Rings and Algebras. $3 274818
650 2 4 $a Category Theory, Homological Algebra. $3 275954
650 2 4 $a Ordinary Differential Equations. $3 273778
650 2 4 $a Partial Differential Equations. $3 274075
700 1 $a Iohara, Kenji. $3 509933
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