We showcase applications of nonlinear algebra in the sciences and engineering. Our review
is organized into eight themes: polynomial optimization, partial differential equations …

We study the asymptotic behavior of the Castelnuovo–Mumford regularity along chains of
graded ideals in increasingly larger polynomial rings that are invariant under the action of …

Symmetric ideals in increasingly larger polynomial rings that form an ascending chain are
investigated. We focus on the asymptotic behavior of codimensions and projective …

Recently, chains of increasing symmetric ideals have attracted considerable attention. In this
note, we summarize some results and open problems concerning the asymptotic behavior of …

We show that if X n is a variety of c× n-matrices that is stable under the group Sym⁡([n]) of
column permutations and if forgetting the last column maps X n into X n-1, then the number …

The setting of this article is nonparametric algebraic statistics. We study moment varieties of
conditionally independent mixture distributions on. These are the secant varieties of toric …

Abstract Every Grassmannian, in its Plücker embedding, is defined by quadratic
polynomials. We prove a vast, qualitative, generalisation of this fact to what we call Plücker …

Algorithmic computation in polynomial rings is a classical topic in mathematics. However,
little attention has been given to the case of rings with an infinite number of variables until …

We study chains of lattice ideals that are invariant under a symmetric group action. In our
setting, the ambient rings for these ideals are polynomial rings which are increasing in …

We extend the theory of Koszul and Buchsbaum-Eisenbud complexes to modules over
commutative OI-algebras and show that they still have the familiar properties of the classical …