Algebraic matroids in action

Authors: Zvi Rosen, Jessica Sidman, and Louis Theran
Journal: The American Mathematical Monthly, 2020.
Full text: arXiv DOI

In recent years, surprising connections between applications including algebraic statistics and the rigidity of bar-and-joint frameworks have sparked a resurgence of interest in various notions of algebraic independence, which may be formalized by the notion of an algebraic matroid. In each of these settings the fundamental problem is to determine the extent to which certain unknowns depend algebraically on given data. We give an introduction to the theory of algebraic matroids motivated by examples that are accessible with an undergraduate background in mathematics and that illustrate the breadth of their potential.