Related papers: Cutting Corners

We explicitly construct new subgroups of the mapping class groups of an uncountable collection of infinite-type surfaces, including, but not limited to, free groups, Baumslag-Solitar groups, mapping class groups of other surfaces, and a…

We consider the problem of deciding the satisfiability of quantifier-free formulas in the theory of finite sets with cardinality constraints. Sets are a common high-level data structure used in programming; thus, such a theory is useful for…

We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…

We continue the study of non-invertible topological dynamical systems with expanding behavior. We introduce the class of {\em finite type} systems which are characterized by the condition that, up to rescaling and uniformly bounded…

In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of each pair of bodies is bounded and every subfamily of size five…

Hughes has defined a class of groups, which we call FSS (finite similarity structure) groups. Each FSS group acts on a compact ultrametric space by local similarities. The best-known example is Thompson's group V. Guided by previous work on…

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…

We propose a novel construction of finite hypergraphs and relational structures that is based on reduced products with Cayley graphs of groupoids. To this end we construct groupoids whose Cayley graphs have large girth not just in the usual…

This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…

We introduce a flexible, categorical framework for large-scale geometry that clarifies basic behaviour of the metric Rips filtration and streamlines some constructions in geometric group theory. The paper has two main parts. First, we…

In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…

Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…

Let ${\mathcal P}\subset{\mathbb Z}^2$ be a convex polygon with each vertex in it labeled by an element from a finite set and such that the labeling of each vertex $v\in {\mathcal P}$ is uniquely determined by the labeling of all other…

We explore the relationship between subgroups and the possible shifts of finite type (SFTs) that can be defined on the group. In particular, we investigate two group invariants, weak periodicity and strong periodicity, defined via symbolic…

We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit…

A convex geometry is a closure space satisfying the anti-exchange axiom. For several types of algebraic convex geometries we describe when the collection of closed sets is order scattered, in terms of obstructions to the semilattice of…

We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable…

While faces of a polytope form a well structured lattice, in which faces of each possible dimension are present, this is not true for general compact convex sets. We address the question of what dimensional patterns are possible for the…

We show that the group of type-preserving automorphisms of any irreducible semi-regular thick right-angled building is abstractly simple. When the building is locally finite, this gives a large family of compactly generated (abstractly)…

We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…