Related papers: Scattered Spaces in Galois Geometry

In this work, we study the geodesics of the space of certain geometrically and physically motivated subspaces of the space of immersed curves endowed with a first order Sobolev metric. This includes elastic curves and also an extension of…

This paper examines the concept of gluing, placing it within its most general categorical context and tracing its foundational role in the broader architecture of algebraic geometry.

This is a survey article on classical groups (over arbitrary division rings) and their geometries.

The aim of this paper is to establish a theory of Galerkin approximations to the space of convex and compact subsets of $\R^d$ with favorable properties, both from a theoretical and from a computational perspective. These Galerkin spaces…

Some companions of Gruss inequality in inner product spaces and applications for integrals are given.

We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.

This paper collects many results on galoisian ideals and Galois theory.

The paper has a form of a survey and consists of three parts. It is focused on the relationship between the many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on the important model-theoretic concepts.…

This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.

Topos properties of the category of covering groupoids over a fixed groupoid are discussed. A classification result for connected covering groupoids over a fixed groupoid analogous to the fundamental theorem of Galois theory is given.

Our paper develops a theory of Poisson slices and a uniform approach to their partial compactifications. The theory in question is loosely comparable to that of symplectic cross-sections in real symplectic geometry.

The scattering transform is a multilayered, wavelet-based transform initially introduced as a model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance…

While geometry with transcendental curves, like the Quadratrix of Hippias and the Spiral of Archimedes, played a significant role in our modern developments of geometry and algebra. The investigation has fallen off in the modern era despite…

The main aim of this work is to present the interpretation of the Ising type models as a kind of field theory in the framework of noncommutative geometry. We present the method and construct sample models of field theory on discrete spaces…

Recent work in higher algebra allows the reinterpretation of a classical description of the Eilenberg-MacLane spectrum $H\mathbb{Z}$ as a Thom spectrum, in terms of a kind of derived Galois theory. This essentially expository talk…

In this paper, we introduce round and sleek topological spaces and study their properties.

Some sharp inequalities of Gruss type for sequences of vectors in real or complex normed linear spaces are obtained. Applications for the discrete Fourier and Mellin transform are given. Estimates for polynomials with coefficients in normed…

An exposition of the basic geometry of twistor integrals, intended for mathematicians.

This is an expository article on the techniques of quantization as they are applied to Gromov-Witten theory and related areas.

Distance Geometry is based on the inverse problem that asks to find the positions of points, in a Euclidean space of given dimension, that are compatible with a given set of distances. We briefly introduce the field, and discuss some open…