



LEADER 
03728nmm a2200457 u 4500 
001 
EB001894401 
003 
EBX01000000000000001057548 
005 
00000000000000.0 
007 
cr 
008 
200303  eng 
020 


a 9783030264543

100 
1 

a Iohara, Kenji
e [editor]

245 
0 
0 
a Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers
h Elektronische Ressource
c edited by Kenji Iohara, Philippe Malbos, MasaHiko Saito, Nobuki Takayama

250 


a 1st ed. 2020

260 


a Cham
b Springer International Publishing
c 2020, 2020

300 


a XI, 371 p. 56 illus., 1 illus. in color
b online resource

505 
0 

a Part I First Byway: Gröbner Bases  1 From Analytical Mechanical Problems to Rewriting Theory Through M. Janet  2 Gröbner Bases in Dmodules: Application to BernsteinSato Polynomials  3 Introduction to Algorithms for DModules with Quiver DModules  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 DeligneSimpson Problems  9 Applications of Quiver Varieties to Moduli Spaces of Connections on P1

653 


a Associative Rings and Algebras

653 


a Algebraic Geometry

653 


a Homological algebra

653 


a Rings (Algebra)

653 


a Algebra

653 


a Field theory (Physics)

653 


a Partial Differential Equations

653 


a Associative rings

653 


a Category Theory, Homological Algebra

653 


a Algebraic geometry

653 


a Partial differential equations

653 


a Field Theory and Polynomials

653 


a Ordinary Differential Equations

653 


a Differential equations

653 


a Category theory (Mathematics)

700 
1 

a Malbos, Philippe
e [editor]

700 
1 

a Saito, MasaHiko
e [editor]

700 
1 

a Takayama, Nobuki
e [editor]

041 
0 
7 
a eng
2 ISO 6392

989 


b Springer
a Springer eBooks 2005

490 
0 

a Algorithms and Computation in Mathematics

856 
4 
0 
u https://doi.org/10.1007/9783030264543?nosfx=y
x Verlag
3 Volltext

082 
0 

a 512.3

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
