Algebraic aspects of hypergeometric differential equations

Abstract

We review some classical and modern aspects of hypergeometric differential equations, including $A$-hypergeometric systems of Gel'fand, Graev, Kapranov and Zelevinsky. Some recent advances in this theory, such as Euler-Koszul homology, rank jump phenomena, irregularity questions and Hodge theoretic aspects are discussed with more details. We also give some applications of the theory of hypergeometric systems to toric mirror symmetry.

References in corpus (7)

• Irregularity of hypergeometric systems via slopes along coordinate subspaces
• Feynman integrals as A-hypergeometric functions
• Hypergeometric D-modules and twisted Gauss-Manin systems
• Hypergeometric Series Representations of Feynman Integrals by GKZ Hypergeometric Systems
• GKZ-hypergeometric systems for Feynman integrals
• Dualizing, projecting, and restricting GKZ systems
• Periods of Feynman Diagrams and GKZ D-Modules

Cited by in corpus (3)

• On Feynman graphs, matroids, and GKZ-systems
• Algebraic Analysis of the Hypergeometric Function 1F1 of a Matrix Argument
• Nonlinear Algebra and Applications