Despite the success of batch normalization (BatchNorm) and a plethora of its variants, the
exact reasons for its success are still shady. The original BatchNorm article explained it as a …

We construct explicit deterministic extractors for polynomial images of varieties, that is,
distributions sampled by applying a low-degree polynomial map f: F qr→ F qn to an element …

Batch Normalization (BatchNorm) is an effective architectural component in deep learning
models that helps to improve model performance and speed up training. However, it has …

We introduce the problem of constructing explicit variety evasive subspace families. Given a
family F of subvarieties of a projective or affine space, a collection H of projective or affine k …

We prove various characterisations for the Cohen–Macaulay property for the invariant ring k
[x 1,…, xn] G, where k is a PID. We also show that, except for one case, all the invariant rings …

We show that any abelian variety over a finite field is covered by a Jacobian whose
dimension is bounded by an explicit constant. We do this by first proving an effective and …

We prove an interpolation result for homogeneous polynomials over the integers, or more
generally for PIDs with finite residue fields. Previous proofs of this result use the well-known …

Good rings and homogeneous polynomials Page 1 J CA JOURNAL OF COMMUTATIVE
ALGEBRA Volume 14 (2022), No. 4, 527–552 DOI: 10.1216/jca.2022.14.527 © Rocky Mountain …

The aim of this thesis is to study the action of a finite group G on a polynomial ring over a
principal ideal domain (PID). We focus on finding the ring of invariants under this action and …

Consider a Noetherian domain R and a finite group G⊆ G ln (R). We prove that if the ring of
invariants R [x 1,…, xn] G is a Cohen-Macaulay ring, then it is generated as an R-algebra by …