Related papers: Hilbert Coefficients and Sally Modules: A Survey o…
The aim of this paper is twofold. First we prove a theorem of extension of sections of a coherent subquotient of a hermitian vector bundle on a complex analytic space with control of the norms, without any of the smoothness assumptions that…
We develop a theory of Hilbert $\widetilde{\C}$-modules by investigating their structural and functional analytic properties. Particular attention is given to finitely generated submodules, projection operators, representation theorems for…
In this paper, certain classes of Hilbert spaces of Dirichlet series with weighted norms and their corresponding multiplier algebras will be explored. For a sequence $\{w_n\}_{n=n_0}^\infty $ of positive numbers, define \[\mathcal…
This paper aims to provide several relations between Bass and Betti numbers of a given module and its deficiency modules. Such relations and the tools used throughout allow us to generalize some results of Foxby, characterize Cohen-Macaulay…
The problem of invariance and self-similarity in Z-modules is investigated. For a selection of examples relevant to quasicrystals, especially Fibonacci modules, we determine the semigroup of self-similarities and encapsulate the number of…
Using invariants from commutative algebra to count geometric objects is a basic idea in singularities. For example, the multiplicity of an ideal is used to count points of intersection of two analytic sets at points of non-transverse…
We discuss the K\"ahler quantization of moduli spaces of vortices in line bundles over compact surfaces $\Sigma$. This furnishes a semiclassical framework for the study of quantum vortex dynamics in the Schr\"odinger-Chern-Simons model. We…
We study numerical invariants associated with the reduction of singularities of holomorphic foliation germs on $(\mathbb{C}^2, 0)$. Building on our previous work on generalized curve foliations, we extend explicit formulas for several…
Spurred by the influential work of Viola (Journal of Computing 2012), the past decade has witnessed an active line of research into the complexity of (approximately) sampling distributions, in contrast to the traditional focus on the…
We propose an approach to obtaining explicit estimates on the resolvent of hypocoercive operators by using Schur complements, rather than from an exponential decay of the evolution semigroup combined with a time integral. We present…
In this paper we analyze the Hilbert boundary-value problem of the theory of analytic functions for an $(N+1)$-connected circular domain. An exact series-form solution has already been derived for the case of continuous coefficients.…
The Shapley effects are global sensitivity indices: they quantify the impact of each input variable on the output variable in a model. In this work, we suggest new estimators of these sensitivity indices. When the input distribution is…
This is a review article exploring similarities between moduli of quiver representations and moduli of vector bundles over a smooth projective curve. After describing the basic properties of these moduli problems and constructions of their…
We propose some conjectures on the integrality properties related to the variation of Mahler measures, inspired by the results in the elliptic curve case by Rodriguez Villegas, Stienstra and Zagier.
The notion of modular covariance is reviewed and the reconstruction of the Poincar\'e group extended to the low-dimensional case. The relations with the PCT symmetry and the Spin and Statistics theorem are described.
We introduce the notion of numerical functors to generalise Eilenberg & MacLane's polynomial functors to modules over a binomial base ring. After shewing how these functors are encoded by modules over a certain ring, we record a precise…
We study the modular resolution method using new tools called polynumbers and polyseries, introduced by Prof. Wildberger N.J. We try to prove an equivalence theorem of the existence and the uniqueness of the solutions of the modular…
We study the behavior of multidegrees in families and the existence of numerical criteria to detect integral dependence. We show that mixed multiplicities of modules are upper semicontinuous functions when taking fibers and that projective…
Many concepts of Fourier analysis on Euclidean spaces rely on the specification of a frequency point. For example classical Littlewood Paley theory decomposes the spectrum of functions into annuli centered at the origin. In the presence of…
A basis of quasi-invariant module over invariants is explicitly constructed for the two-dimensional Coxeter systems with arbitrary multiplicities. It is proved that this basis consists of $m$-harmonic polynomials, thus the earlier results…