Related papers: Framed combinatorial topology
Tropical algebraic geometry is an active new field of mathematics that establishes and studies some very general principles to translate algebro-geometric problems into purely combinatorial ones. This expository paper gives an introduction…
Over the past two decades, topological data analysis has emerged as a field of applied mathematics with new applications and algorithmic developments appearing rapidly. Two fundamental computations in this field are persistent homology and…
Torsion sensitive intersection homology was introduced to unify several versions of Poincare duality for stratified spaces into a single theorem. This unified duality theorem holds with ground coefficients in an arbitrary PID and with no…
In the philosophical literature, symmetries of physical theories are most often interpreted within the general doctrine called 'Sophistication'. Roughly speaking, it says that models related by symmetries can peacefully co-exist while…
We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory. We suggest a unifying approach using operators where we allow the…
Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images, reconciling state of the art performance with strong theoretical guarantees. However, tensor-based…
Topological phases of matter are one of the hallmarks of quantum condensed matter physics. One of their striking features is a bulk-boundary correspondence wherein the topological nature of the bulk manifests itself on boundaries via exotic…
We give a general notion of combinatory completeness with respect to a faithful cartesian club and use it systematically to obtain characterisations of a number of different kinds of applicative system. Each faithful cartesian club…
We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…
We prove that some of the basic differential functions appearing in the (unramified) theory of arithmetic differential equations, especially some of the basic differential modular forms in that theory, arise from a "ramified situation".…
We propose a definition of computable manifold by introducing computability as a structure that we impose to a given topological manifold, just in the same way as differentiability or piecewise linearity are defined for smooth and PL…
The immensely fruitful concept of Grothendieck topology or covering issued from the efforts of algebraic geometers to study "sheaf-like" objects defined on categories more general than the lattice of open sets on a topological space. In the…
We develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets are tame: there is a good notion of dimension on definable…
There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…
We develop a theory of umkehr maps for twisted generalized homology theories. In this theory, interesting umkehr maps, including generalizations of important classical ones, are induced by cartesian morphisms of a certain category opfibred…
Homological algebra of modules over posets is developed, as closely parallel as possible to that of finitely generated modules over noetherian commutative rings, in the direction of finite presentations and resolutions. Centrally at issue…
Motivated by questions in biological classification, we discuss some elementary combinatorial and computational properties of certain set systems that generalize hierarchies, namely, 'patchworks', 'weak patchworks', 'ample patchworks' and…
Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (both classical and intuitionistic), and forcing. In this work,…
Topology is a fundamental aspect of quantum physics, and it has led to key breakthroughs and results in various fields of quantum materials. In condensed matters, this has culminated in the recent discovery of symmetry-protected topological…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…