Related papers: Stein degree of proper morphisms
We detail an approach to develop Stein's method for bounding integral metrics on probability measures defined on a Riemannian manifold $\mathbf M$. Our approach exploits the relationship between the generator of a diffusion on $\mathbf M$…
The aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner System $S(t,n,v)$ we associate two ideals, in a suitable polynomial ring, defining a Steiner…
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
Degrees of freedom is a fundamental concept in statistical modeling, as it provides a quantitative description of the amount of fitting performed by a given procedure. But, despite this fundamental role in statistics, its behavior not…
The Turing degree spectrum of a countable structure $\mathcal{A}$ is the set of all Turing degrees of isomorphic copies of $\mathcal{A}$. The Turing degree of the isomorphism type of $\mathcal{A}$, if it exists, is the least Turing degree…
Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion…
We classify Artin-Schreier extensions of valued fields with non-trivial defect according to whether they are connected with purely inseparable extensions with non-trivial defect, or not. We use this classification to show that in positive…
A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…
We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first-order…
We study arithmetic degree of a dominant rational self-map on a smooth projective variety over a function field of characteristic zero. We see that the notion of arithmetic degree and some related problems over function fields are…
We study the theory specialisations in algebraic geometry from a model theoretic viewpoint. In particular we investigate universality and maximality of specialisations in algebraic geometry.
The Euclidean distance degree of an algebraic variety is a well-studied topic in applied algebra and geometry. It has direct applications in geometric modeling, computer vision, and statistics. We use non-proper Morse theory to give a…
We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…
Recently, two first authors have introduced a group invariant, which is related to the number of elements $x$ and $y$ of a finite group $G$ such that $x\wedge y=1$ in the exterior square $G\wedge G$ of $G$. Research on this probability…
In this paper, we present a refined version of the (classical) Stein inequality for the Fourier transform, elevating it to a new level of accuracy. Furthermore, we establish extended analogues of a more precise version of the Stein…
Graded rings provide a natural algebraic framework for encoding symmetry via decompositions into homogeneous components indexed by a group, together with multiplication rules reflecting the group operation. Among graded rings, strongly…
Let $k$ be a non-archimedean complete valued field and $X$ be a $k$-analytic space in the sense of Berkovich. In this note, we prove the equivalence between three properties: 1) for every complete valued extension $k'$ of $k$, every…
We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed…
Birational properites of generically finite morphisms $X\rightarrow Y$ of algebraic varieties can be understood locally by a valuation of the function field of $X$. In finite extensions of algebraic local rings in characteristic zero…
In the past the first named author has studied to what extent the integral trace can characterize a number field beyond what the discriminant does. The cases of cyclic number fields and non-totally real fields are more or less settled,…