Related papers: Closed graph theorems for bornological spaces

It is shown that graphs that generalize the ADE Dynkin diagrams and have appeared in various contexts of two-dimensional field theory may be regarded in a natural way as encoding the geometry of a root system. After recalling what are the…

The aim of this paper is to present a survey of some recent results obtained in the study of spaces with asymmetric norm. The presentation follows the ideas from the theory of normed spaces (topology, continuous linear operators, continuous…

We introduce and study certain topological spaces associated with connected rooted graphs. These spaces reflect combinatorial and order theoretic properties of the underlying graph and relate in the case of hyperbolic graphs to Gromov's…

We show that a sufficiently large graph of bounded degree can be decomposed into quasi-homogeneous pieces. The result can be viewed as a "finitarization" of the classical Farrell-Varadarajan Ergodic Decomposition Theorem.

Locally-biased graph algorithms are algorithms that attempt to find local or small-scale structure in a large data graph. In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph…

The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by…

In trying to generalize the classic Sylvester-Gallai theorem and De Bruijn-Erd\H{o}s theorem in plane geometry, lines and closure lines were previously defined for metric spaces and hypergraphs. Both definitions do not obey the geometric…

We study the category whose objects are graphs of fixed genus and whose morphisms are contractions. We show that the corresponding contravariant module categories are Noetherian and we study two families of modules over these categories.…

The area of graph property testing seeks to understand the relation between the global properties of a graph and its local statistics. In the classical model, the local statistics of a graph is defined relative to a uniform distribution…

In this paper, we develop a geometric approach to study derived tame finite dimensional associative algebras, based on the theory of non-commutative nodal curves.

We give proofs of de Rham comparison isomorphisms for rigid-analytic varieties, with coefficients and in families. This relies on the theory of perfectoid spaces. Another new ingredient is the pro-etale site, which makes all constructions…

A graph-theoretic method is introduced for analyzing fermion mass spectra in latticized theory-space models, including chain models arising from dimensional deconstruction. Fermion mass terms are mapped to bipartite graphs, with fields as…

The theorem of Greenberg-Kazhdan-Drinfeld describes the formal neighborhood of a closed arc. After giving a complete proof with examples, two possible versions for the relative case of the theorem are discussed. Each one is shown to hold…

Finite simple graphs are a playground for classical areas of mathematics. We illustrate this by looking at some theorems. These are slightly enhanced preparation notes for a talk given at the joint AMS meeting of January 16, 2014 in…

We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie…

This article, addressed to a general audience of functional analysts, is intended to be an illustration of a few basic principles from `noncommutative functional analysis', more specifically the new field of {\em operator spaces.} In our…

We provide several families of compact complex curves embedded in smooth complex surfaces such that no neighborhood of the curve can be embedded in an algebraic surface. Different constructions are proposed, by patching neighborhoods of…

For classes of topological vector spaces, we analyze under which conditions open-mapping, continuous-inverse, and closed-graph properties are equivalent. Here, closure under quotients with closed subspaces and closure under closed graphs…

Inspired by the work of Cherry, we introduce and study a new notion of Brody hyperbolicity for rigid analytic varieties over a non-archimedean field $K$ of characteristic zero. We use this notion of hyperbolicity to show the following…

We present recent advances in harmonic analysis on infinite graphs. Our approach combines combinatorial tools with new results from the theory of unbounded Hermitian operators in Hilbert space, geometry, boundary constructions, and spectral…