Related papers: Constructing endperiodic loxodromics of infinite-t…

We will announce two theorems. The first theorem will classify all topological types of degenerate fibers appearing in one-parameter families of Riemann surfaces, in terms of ``pseudoperiodic'' surface homeomorphisms. The second theorem…

For a Z-cover of a translation surface, which is a lattice surface, and which admits infinite strips, we prove that almost every direction for the straightline flow is ergodic.

The aim of this work is to offer a family of invariants that allows us to classify finite potent endomorphisms on arbitrary vector spaces, generalizing the classification of endomorphisms on finite-dimensional vector spaces. As a particular…

We give cohomological criteria for logarithmic good reduction of elliptic surfaces up to modification. Along the way, we prove several more general results about such surfaces in positive characteristic, as well as about log smooth…

We study endomorphisms and derivations of infinite dimensional cyclic Leibniz algebra.

We prove that for any infinite-type orientable surface S there exists a collection of essential curves {\Gamma} in S such that any homeomorphism that preserves the isotopy classes of the elements of {\Gamma} is isotopic to the identity. The…

A digraph is connected-homogeneous if any isomorphism between finite connected induced subdigraphs extends to an automorphism of the digraph. We consider locally-finite connected-homogeneous digraphs with more than one end. In the case that…

The systole of a hyperbolic surface is bounded by a logarithmic function of its genus. This bound is sharp, in that there exist sequences of surfaces with genera tending to infinity that attain logarithmically large systoles. These are…

Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…

We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…

In this note, we construct three new infinite families of surfaces of general type with canonical map of degree 2 onto a surface of general type. For one of these families the canonical system has base points.

Suppose $G$ is a finitely generated infinite group, and $\mathcal G$ is a graph of groups decomposition of $G$ such that the edge groups are finite. This paper establishes that the topology of the Floyd boundary of $G$ is uniquely…

We expand the dictionary between the action of a torus homeomorphism on the fine curve graph and its rotation set. More precisely, we show that the fixed points at infinity of a loxodromic element determine the rotation set up to scale. A…

We completely describe the Gromov-Hausdorff closure of the class of length spaces being homeomorphic to a fixed closed surface.

We calculate the automorphism group of certain Enriques surfaces. The Enriques surfaces that we investigate include very general $n$-nodal Enriques surfaces and very general cuspidal Enriques surfaces. We also describe the action of the…

We prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.

A constructive method is given for obtaining cospectral vertices in undirected graphs, along with an operation that preserves this construction. We prove that the construction yields cospectral vertices, as well as strongly cospectral…

We study two actions of big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. The first two…

Two of the natural topologies for infinite graphs with edge-ends are Etop and Itop. In this paper, we study and characterize them. We show that Itop can be constructed by inverse limits of inverse systems of graphs with finitely many…

We show that any infinite-type surface without planar ends admits arbitrarily large families of length isospectral hyperbolic structures. If the surface has infinite genus and its space of ends is self-similar, we construct an uncountable…