國立虎尾科技大學 |

Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers/ edited by Kenji Iohara, Philippe Malbos, Masa-Hiko Saito, Nobuki Takayama.
其他作者:	Takayama, Nobuki.
面頁冊數:	XI, 371 p. 56 illus., 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Partial Differential Equations. -
電子資源:	https://doi.org/10.1007/978-3-030-26454-3
ISBN:	9783030264543

Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers
Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers[electronic resource] /edited by Kenji Iohara, Philippe Malbos, Masa-Hiko Saito, Nobuki Takayama. - 1st ed. 2020. - XI, 371 p. 56 illus., 1 illus. in color.online resource. - Algorithms and Computation in Mathematics,281431-1550 ;. - Algorithms and Computation in Mathematics,27.

Part I First Byway: Gröbner Bases -- 1 From Analytical Mechanical Problems to Rewriting Theory Through M. Janet -- 2 Gröbner Bases in D-modules: Application to Bernstein-Sato Polynomials -- 3 Introduction to Algorithms for D-Modules with Quiver D-Modules -- 4 Noncommutative Gröbner 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 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.

ISBN: 9783030264543

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

671119
Partial Differential Equations.

LC Class. No.: QA247-247.45

Dewey Class. No.: 512.3

Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers
LDR:03594nam a22004095i 4500 001 1025284
003 DE-He213
005 20200702012845.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030264543 $9 978-3-030-26454-3
024 7 $a 10.1007/978-3-030-26454-3 $2 doi
035 $a 978-3-030-26454-3
050 4 $a QA247-247.45
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.3 $2 23
245 1 0 $a Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers $h [electronic resource] / $c edited by Kenji Iohara, Philippe Malbos, Masa-Hiko Saito, Nobuki Takayama.
250 $a 1st ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a XI, 371 p. 56 illus., 1 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Algorithms and Computation in Mathematics, $x 1431-1550 ; $v 28
505 0 $a Part I First Byway: Gröbner Bases -- 1 From Analytical Mechanical Problems to Rewriting Theory Through M. Janet -- 2 Gröbner Bases in D-modules: Application to Bernstein-Sato Polynomials -- 3 Introduction to Algorithms for D-Modules with Quiver D-Modules -- 4 Noncommutative Gröbner 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 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.
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Ordinary Differential Equations. $3 670854
650 2 4 $a Category Theory, Homological Algebra. $3 678397
650 2 4 $a Associative Rings and Algebras. $3 672306
650 2 4 $a Algebraic Geometry. $3 670184
650 1 4 $a Field Theory and Polynomials. $3 672025
650 0 $a Partial differential equations. $3 1102982
650 0 $a Differential equations. $3 527664
650 0 $a Homological algebra. $3 1255326
650 0 $a Category theory (Mathematics). $3 1255325
650 0 $a Rings (Algebra). $3 685051
650 0 $a Associative rings. $3 893564
650 0 $a Algebraic geometry. $3 1255324
650 0 $a Field theory (Physics). $3 685987
650 0 $a Algebra. $2 gtt $3 579870
700 1 $a Takayama, Nobuki. $4 edt $4 http://id.loc.gov/vocabulary/relators/edt $3 680692
700 1 $a Saito, Masa-Hiko. $e editor. $4 edt $4 http://id.loc.gov/vocabulary/relators/edt $3 1321529
700 1 $a Malbos, Philippe. $e editor. $4 edt $4 http://id.loc.gov/vocabulary/relators/edt $3 1321528
700 1 $a Iohara, Kenji. $4 edt $4 http://id.loc.gov/vocabulary/relators/edt $3 783134
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030264536
776 0 8 $i Printed edition: $z 9783030264550
776 0 8 $i Printed edition: $z 9783030264567
830 0 $a Algorithms and Computation in Mathematics, $x 1431-1550 ; $v 27 $3 1281446
856 4 0 $u https://doi.org/10.1007/978-3-030-26454-3
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)