This paper surveys and develops links between polynomial invariants of finite groups,
factorization theory of Krull domains, and product-one sequences over finite groups. The …

We study a class of orbit recovery problems in which we observe independent copies of an
unknown element of R p, each linearly acted upon by a random element of some group …

We consider Galois/monodromy groups arising in computer vision applications, with a view
toward building more efficient polynomial solvers. The Galois/monodromy group allows us to …

Degree bounds for algebra generators of invariant rings are a topic of longstanding interest
in invariant theory. We study the analogous question for field generators for the field of …

A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose
elements distinguish between any two orbits that can be distinguished using invariants. In …

We consider finite dimensional representations of the dihedral group D2p over an
algebraically closed field of characteristic two where p is an odd prime and study the …

It is proved that the universal degree bound for separating polynomial invariants of a finite
abelian group (in non-modular characteristic) is typically strictly smaller than the universal …

Roughly speaking, a separating algebra is a subalgebra of the ring of invariants whose
elements distinguish between any two orbits that can be distinguished using invariants. In …

We define a generic separating set of invariant functions (aka a weak functional basis) for
tensors. We then produce two generic separating sets of polynomial invariants for three …

The main purpose of this paper is to give a survey of algorithms in invariant theory, with
emphasis on nonreductive groups and on recent developments. But the article has some …