Gkz system in mathematics
WebApr 15, 2024 · To a torus action on a complex vector space, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, which are now called the GKZ … WebGel’fand, Kapranov, and Zelevinsky (GKZ systems). These functions generalize the classical hypergeometric functions of Gauss, Horn, Appell, and Lauricella. We will emphasize the alge-braic methods of Saito, Sturmfels, and Takayama to construct hypergeometric …
Gkz system in mathematics
Did you know?
WebJan 17, 2024 · In such cases, the GKZ-system can inherit a mixed Hodge module structure. I will then explain work with Thomas Reichelt that computes the weight filtration of this … WebAug 7, 2012 · To a torus action on a complex vector space, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, called the GKZ hypergeometric system. Its solutions are GKZ hypergeometric functions. We study the -adic counterpart of the GKZ hypergeometric system, which we call the -adic GKZ hypergeometric sheaf.
WebApr 11, 2024 · The GKZ hypergeometric functions are defined as solutions to system of differential equations associated with the ( {\mathcal {A}},c) -hypergeometric structures, first introduced and studied in [ 2, 4, 5 ]. The GKZ hypergeometric structure is defined by the following data. We choose an N -element subset WebDec 15, 2024 · :: It returns the Pfaff equation for the GKZ system defined by A and Beta with respect to cocycles defined by Rvec . return a list of coefficients of the Pfaff equation …
WebThe Gelfand–Kapranov–Zelevinsky hypergeometric system (GKZ) associated to the set A and parame- ter βis a system of differential equations on the function Φ(z),z= (z1,...,zn) ∈ Cn,consisting of the binomial equations Y j,lj>0 ∂ ∂zj l j− Y j,lj<0 ∂ ∂zj −l j Φ = 0, l∈ L, and the linear equations −β+ Xn j=1 vjzj ∂ ∂zj Φ = 0. WebNov 23, 2024 · Utilizing the GKZ system and its relation to $D$-module theory, we propose a novel method for obtaining differential equations for master integrals.
WebNov 10, 2015 · In the paper [RS15a], this kind of result is pushed further by not only showing that certain regular GKZ-systems underly mixed Hodge modules but proving that the associated Hodge filtration is...
WebA GKZ A-hypergeometric system (or a GKZ A-hypergeometric D-module), in-troduced by Gel’fand, Graev, Kapranov, and Zelevinskii [3,5], is a system of linear partial … rice university office of sponsored researchWeb2. Better behaved GKZ hypergeometric systems In this section, we give an overview of the so-called better behaved GKZ hypergeometric systems which were de ned in [6]. When the rank of the lattice N in the de nition of the systems is two, we show that a solution to the system can be given in the form of contour integrals which will be rice university off campus meal planWebSep 12, 2024 · As a corollary we get a purely combinatorial formula for the length of the underlying (regular) holonomic GKZ-system, irrespective of homogeneity. In dimension … rice university omar syedWebAug 27, 2015 · Roughly defined, the GKZ (Gelfand-Kapranov-Zelevinsky) systems are classes of differential equations that can be solved in terms of generalised … rice university office of technology transferWebJul 1, 2024 · In order to define such GKZ system, we consider the polynomial obtained from the Symanzik polynomials $g=\mathcal{U}+\mathcal{F}$ as having indeterminate … redis binary dataWebApr 24, 2014 · Laurent polynomials, GKZ-hypergeometric systems and mixed Hodge modules Part of: Families, fibrations Singularities Deformations of analytic structures … rice university oissWebDepartment of Mathematics Columbia University New York, NY 10027 November 5, 2007 Contents 1 Introduction 1 2 Intersection formulae 5 3 Product formulae 13 4 Modularity in … redis bing