14 citations · 52 across the 18 of their papers we have counts for
18 papers
Border Bases in the Rational Weyl Algebra
Carlos Rodriguez, Anna-Laura Sattelberger
Border bases are a generalization of Gröbner bases for zero-dimensional ideals in polynomial rings. In this article, we introduce border bases for a non-commutative ring of linear…
Connection Matrices in Macaulay2
Paul Görlach, Joris Koefler, Anna-Laura Sattelberger +4
In this article, we describe the theoretical foundations of the Macaulay2 package ConnectionMatrices and explain how to use it. For a left ideal in the Weyl algebra that is of fini…
Algebraic and Positive Geometry of the Universe: from Particles to Galaxies
Claudia Fevola, Anna-Laura Sattelberger
In recent years, the intersection of algebra, geometry, and combinatorics with particle physics and cosmology has led to significant advances. Central to this progress is the twofo…
Differential Equations for Moving Hyperplane Arrangements
Anaëlle Pfister, Anna-Laura Sattelberger
We investigate Mellin integrals of products of hyperplanes, raised to an individual power each. We refer to the resulting functions as combinatorial correlators. We investigate the…
Algebraic Approaches to Cosmological Integrals
Claudia Fevola, Guilherme L. Pimentel, Anna-Laura Sattelberger +1
Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rationa…
Geometry of Linear Neural Networks: Equivariance and Invariance under Permutation Groups
Kathlén Kohn, Anna-Laura Sattelberger, Vahid Shahverdi
The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invaria…
-Module Techniques for Solving Differential Equations in the Context of Feynman Integrals
Johannes Henn, Elizabeth Pratt, Anna-Laura Sattelberger +1
Feynman integrals are solutions to linear partial differential equations with polynomial coefficients. Using a triangle integral with general exponents as a case in point, we compa…
D-Algebraic Functions
Rida Ait El Manssour, Anna-Laura Sattelberger, Bertrand Teguia Tabuguia
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure propertie…
Vector Spaces of Generalized Euler Integrals
Daniele Agostini, Claudia Fevola, Anna-Laura Sattelberger +1
We study vector spaces associated to a family of generalized Euler integrals. Their dimension is given by the Euler characteristic of a very affine variety. Motivated by Feynman in…
Bayesian Integrals on Toric Varieties
Michael Borinsky, Anna-Laura Sattelberger, Bernd Sturmfels +1
We explore the positive geometry of statistical models in the setting of toric varieties. Our focus lies on models for discrete data that are parameterized in terms of Cox coordina…
The Shift-Dimension of Multipersistence Modules
Wojciech Chachólski, René Corbet, Anna-Laura Sattelberger
We present the shift-dimension of multipersistence modules and investigate its algebraic properties. This gives rise to a new invariant of multigraded modules over the multivariate…
Nonlinear Algebra and Applications
Paul Breiding, Türkü Özlüm Çelik, Timothy Duff +5
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, a…
Combinatorial Differential Algebra of
Rida Ait El Manssour, Anna-Laura Sattelberger
We link -jets of the affine monomial scheme defined by to the stable set polytope of some perfect graph. We prove that, as varies, the dimension of the coordinate ring…
Maximum Likelihood Estimation from a Tropical and a Bernstein--Sato Perspective
Anna-Laura Sattelberger, Robin van der Veer
In this article, we investigate Maximum Likelihood Estimation with tools from Tropical Geometry and Bernstein--Sato theory. We investigate the critical points of very affine variet…
Algebraic Analysis of the Hypergeometric Function 1F1 of a Matrix Argument
Paul Görlach, Christian Lehn, Anna-Laura Sattelberger
In this article, we investigate Muirhead's classical system of differential operators for the hypergeometric function 1F1 of a matrix argument. We formulate a conjecture for the co…
Algebraic Analysis of Rotation Data
Michael F. Adamer, András C. Lőrincz, Anna-Laura Sattelberger +1
We develop algebraic tools for statistical inference from samples of rotation matrices. This rests on the theory of D-modules in algebraic analysis. Noncommutative Gröbner bases ar…
D-Modules and Holonomic Functions
Anna-Laura Sattelberger, Bernd Sturmfels
In algebraic geometry, one studies the solutions to polynomial equations, or, equivalently, to linear partial differential equations with constant coefficients. These lecture notes…
Topological computation of the Stokes matrices of the weighted projective line
Anna-Laura Sattelberger
The localized Fourier-Laplace transform of the Gauß-Manin system of is a -module, having…