9 citations · 9 across the 2 of their papers we have counts for
9 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…