LEADER 05499nam 22008175 450 001 996418257003316 005 20200702012845.0 010 $a3-030-26454-8 024 7 $a10.1007/978-3-030-26454-3 035 $a(CKB)4100000010474124 035 $a(DE-He213)978-3-030-26454-3 035 $a(MiAaPQ)EBC6119386 035 $a(PPN)242979351 035 $a(EXLCZ)994100000010474124 100 $a20200220d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTwo Algebraic Byways from Differential Equations: Gröbner Bases and Quivers$b[electronic resource] /$fedited by Kenji Iohara, Philippe Malbos, Masa-Hiko Saito, Nobuki Takayama 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XI, 371 p. 56 illus., 1 illus. in color.) 225 1 $aAlgorithms and Computation in Mathematics,$x1431-1550 ;$v28 311 $a3-030-26453-X 327 $aPart 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. 330 $aThis edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types. Although the theory of Gröbner bases was developed in the second half of the 20th century, many works on computational methods in algebra were published well before the introduction of the modern algebraic language. Since then, new algorithms have been developed and the theory itself has greatly expanded. In comparison, diagrammatic methods in representation theory are relatively new, with the quiver varieties only being introduced ? with big impact ? in the 1990s. Divided into two parts, the book first discusses the theory of Gröbner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Gröbner bases to analysis on systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. It then introduces representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line. While no particular reader background is assumed, the book is intended for graduate students in mathematics, engineering and related fields, as well as researchers and scholars. 410 0$aAlgorithms and Computation in Mathematics,$x1431-1550 ;$v28 606 $aAlgebra 606 $aField theory (Physics) 606 $aAlgebraic geometry 606 $aAssociative rings 606 $aRings (Algebra) 606 $aCategory theory (Mathematics) 606 $aHomological algebra 606 $aDifferential equations 606 $aPartial differential equations 606 $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aAlgebra. 615 0$aField theory (Physics). 615 0$aAlgebraic geometry. 615 0$aAssociative rings. 615 0$aRings (Algebra). 615 0$aCategory theory (Mathematics). 615 0$aHomological algebra. 615 0$aDifferential equations. 615 0$aPartial differential equations. 615 14$aField Theory and Polynomials. 615 24$aAlgebraic Geometry. 615 24$aAssociative Rings and Algebras. 615 24$aCategory Theory, Homological Algebra. 615 24$aOrdinary Differential Equations. 615 24$aPartial Differential Equations. 676 $a512.24 702 $aIohara$b Kenji$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aMalbos$b Philippe$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aSaito$b Masa-Hiko$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aTakayama$b Nobuki$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418257003316 996 $aTwo Algebraic Byways from Differential Equations: Gröbner Bases and Quivers$92351483 997 $aUNISA