Related papers: Arcs, hypercubes, and graphs as quotients of proje…
We derive a lower bound on the size of finite non-cyclic quotients of the braid group that is superexponential in the number of strands. We also derive a similar lower bound for nontrivial finite quotients of the commutator subgroup of the…
We use a restriction theorem for Fourier transforms of fractal measures to study projections onto families of planes in R^3 whose normal directions form nondegenerate curves.
We investigate complete arcs of degree greater than two, in projective planes over finite fields, arising from the set of rational points of a generalization of the Hermitian curve. The degree of the arcs is closely related to the number of…
Let X be a Hausdorff quotient of a standard space (that is of a locally compact separable metric space). It is shown that the following are equivalent: (i) X is the image of an irreducible quotient map from a standard space; (ii) X has a…
We continue the study of projective Fra\"iss\'e limits developed by Irwin-Solecki and Panagiotopoulos-Solecki by investigating families of epimorphisms between finite trees and finite rooted trees. Ideas of monotone, confluent, and light…
We show that if a flat group scheme acts properly, with finite stabilizers, on an algebraic space, then a quotient exists as a separated algebraic space. More generally we show any flat groupid for which the family of stabilizers is finite…
We show that all the possible pairs of integers occur as exponents for free or nearly free irreducible plane curves and line arrangements, by producing only two types of simple families of examples. The topology of the complements of these…
By a result of Zucker, every Fra\"iss\'e structure $\bf F$ for which the elements of $\mathrm{Age}(\bf F)$ have finite Ramsey degrees admits a Fra\"iss\'e precompact expansion $\bf F^{*}$ whose age $\mathrm{Age}(\bf F^{*})$ has the Ramsey…
We announce and examine the conjecture that each infinite connected normal Hausdorff space has a quotient homeomorphic to the unit interval, shown to be true with the additional assumption of compactness or local connectedness. Some…
Graphons are analytic objects associated with convergent sequences of dense graphs. Finitely forcible graphons, i.e., those determined by finitely many subgraph densities, are of particular interest because of their relation to various…
We consider weighted graphs with an infinite set of vertices. We show that boundedness of all functions of finite energy can be seen as a notion of `relative compactness' for such graphs and study sufficient and necessary conditions for…
The goal of the paper is to lay the foundation for the qualitative analogue of the classical, quantitative sparse graph limit theory. In the first part of the paper we introduce the qualitative analogues of the Benjamini-Schramm and…
This paper continues a geometric study of Harvey's Complex of Curves, whose ultimate goal is to apply the theory of hyperbolic spaces and groups to algorithmic questions for the Mapping Class Group and geometric properties of Kleinian…
In this paper we describe projective curves and surfaces such that almost all their hyperplane sections are projectively equivalent. Our description is complete for curves and close to being complete for smooth surfaces. In the appendix we…
We construct a wealth of groups that are finitely presented, Frobenius stable, have property (T), but are very far from having property (T$_2$). Our method also shows that property (T$_2$) does not pass to quotients.
We study an infinite class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. This generalizes a sequence of sparse polynomials which arises in a natural way as graph theoretic…
We study new families of curves that are suitable for efficiently parametrizing their moduli spaces. We explicitly construct such families for smooth plane quartics in order to determine unique representatives for the isomorphism classes of…
The cut pseudo-metric on the space of graph limits induces an equivalence relation. The quotient space obtained by collapsing each equivalence class to a point is a metric space with appealing analytic properties. We show that the…
In this paper, the Cartan frames and the equi-affine curvatures are described with the help of the Frenet frames and the Frenet curvatures of a non-null and non-degenerate curve in a 3-dimensional pseudo-Riemannian manifold. The constancy…
We study arc graphs and curve graphs for surfaces of infinite topological type. First, we define an arc graph relative to a finite number of (isolated) punctures and prove that it is a connected, uniformly hyperbolic graph of infinite…