Two Algebraic Byways from Differential Equations: Groebner Bases and Quivers

This edited volume explores differential equations from two perspectives: formal calculus and geometry, using Gröbner bases as a computational tool. It discusses the theory of Gröbner bases, their applications in analyzing systems of partial differential equations, and representations of quivers and quiver varieties. The book is intended for graduate students, researchers, and scholars in mathematics, engineering, and related fields.

Format: Paperback / softback
Length: 371 pages
Publication date: 15 July 2021
Publisher: Springer Nature Switzerland AG

This edited volume presents a captivating collection of lecture notes, delving into differential equations from two distinct perspectives: formal calculus and geometry. Gröbner bases emerge as powerful computational models in algebras of various types, serving as effective tools for solving complex problems. While the theory of Gröbner bases was developed in the latter half of the 20th century, numerous works on computational methods in algebra predate the introduction of the modern algebraic language. Since then, innovative algorithms have been devised, and the theory itself has undergone significant expansion. In contrast, diagrammatic methods in representation theory are relatively new, with quiver varieties only being introduced in the 1990s, making a substantial impact.

The book is structured into two parts. The first part explores the theory of Gröbner bases, focusing on their commutative and noncommutative contexts. It delves into algorithmic aspects and applications of Gröbner bases in analyzing systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. The second part introduces representations of quivers, quiver varieties, and their applications to the moduli spaces of meromorphic connections on the complex projective line.

While no specific reader background is assumed, the book is designed for graduate students in mathematics, engineering, and related fields, as well as researchers and scholars. Its comprehensive coverage and insightful discussions make it an invaluable resource for those interested in advancing their knowledge in this field.

Weight: 587g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030264567
Edition number: 1st ed. 2020