Related papers: Level {\epsilon}
Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…
We introduce and study a notion of algebraic entropy for self-maps of finite length of Noetherian local rings, and develop its properties. We show that it shares the standard properties of topological entropy. For finite self-maps we…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
The main goal of this paper is to reveal the geometric meaning of the maximal number of exceptional values of Gauss maps for several classes of immersed surfaces in space forms, for example, complete minimal surfaces in the Euclidean…
The aim of this article is to give a rigorous geometric interpretation of the completion of a ring with respect to an ideal. To this end, we define the infinitesimal neighbourhood of an immersion of formal schemes as the largest possible…
In this short review, we pay attention to some subtleties in the study of projective representations, contrasting local to global properties and their interplay. The analysis is exposed rigorously, showing and demonstrating the main…
We answer two questions about the topology of end spaces of infinite type surfaces and the action of the mapping class group that have appeared in the literature. First, we give examples of infinite type surfaces with end spaces that are…
The essential subtoposes of a fixed topos form a complete lattice, which gives rise to the notion of a level in a topos. In the familiar example of simplicial sets, levels coincide with dimensions and give rise to the usual notions of…
We relate the topology of the Morse boundary of a group to geometric and algorithmic properties of the group. In particular, we show that a group has $\sigma$-compact Morse boundary if and only if it is Morse local-to-global. We also…
Generalizing a theorem of Campercholi, we characterize, in syntactic terms, the ranges of epimorphisms in an arbitrary class of similar first-order structures (as opposed to an elementary class). This allows us to strengthen a result of…
Materials like paper, consisting of a network of natural fibres, exposed to variations in moisture, undergo changes in geometrical and mechanical properties. This behaviour is particularly important for understanding the hygro-mechanical…
The use of random samples to approximate properties of geometric configurations has been an influential idea for both combinatorial and algorithmic purposes. This chapter considers two related notions---$\epsilon$-approximations and…
Trophic coherence, a measure of a graph's hierarchical organisation, has been shown to be linked to a graph's structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their…
We apply techniques from harmonic analysis to study the $L^p$ norms of Maass forms of varying level on a quaternion division algebra. Our first result gives a candidate for the local bound for the sup norm in terms of the level, which is…
A closed-form expression is obtained for the density of a simple layer, equipotential to an oblate level ellipsoid of revolution in an outer space. The potential of any level spheroid of positive mass with the inward direction of attracting…
The latent space approach to complex networks has revealed fundamental principles and symmetries, enabling geometric methods. However, the conditions under which network topology implies geometricity remain unclear. We provide a…
Many classical results in algebraic geometry arise from investigating some extremal behaviors that appear among projective varieties not lying on any hypersurface of fixed degree. We study two numerical invariants attached to such…
The indicatrix or curvature ellipse and the characteristic curve of a surface in $\mathbf R^4$ are presented, as well as the projective duality connecting them. The characterisation of points in the surfaces as elliptic, parabolic and…
This book is expository and is in Russian. It is shown how in the course of solution of interesting geometric problems (close to applications) naturally appear main notions of algebraic topology (homology groups, obstructions and…
We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense.…