Related papers: Cosmology of Plane Geometry
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
The study of the properties of cosmic structures in the universe is one of the most fascinating subject of the modern cosmology research. Far from being predicted, the large scale structure of the matter distribution is a very recent…
We give a general and nontechnical review of some aspects of noncommutative geometry as a tool to understand the structure of spacetime. We discuss the motivations for the constructions of a noncommutative geometry, and the passage from…
A short survey on applications of algebraic geometry in topological data analysis.
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
This paper presents a geometric approach to the problem of modelling the relationship between words and concepts, focusing in particular on analogical phenomena in language and cognition. Grounded in recent theories regarding geometric…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…
The purpose of this survey article is to introduce the reader to a connection between Logic, Geometry, and Algebra which has recently come to light in the form of an interpretation of the constructive type theory of Martin-L\"of into…
In this thesis we study classical aspects of superconformal field theory via symmetry principles. Specifically, by employing the powerful setup of conformal superspace, we obtain a plethora of new results in the fields of geometric and…
In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.
We present a new cosmological model derived from Loop Quantum Gravity. The formulation is based on a projection of the kinematical Hilbert space of the full theory down to a subspace representing the proper arena for an inhomogeneous…
In this review, we outline the expected tests of gravity that will be achieved at cosmological scales in the upcoming decades. We focus mainly on constraints on phenomenologically parameterized deviations from general relativity, which…
The purpose of this paper is to introduce a version of singular homology based on smooth mappings of manifolds with corners. Although variants of such a theory exists in the literature, we felt that certain points were not adequately…
In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.
We discuss a new geometric construction of port-Hamiltonian systems. Using this framework, we revisit the notion of interconnection providing it with an intrinsic description. Special emphasis on theoretical and applied examples is given…
We aim to bring a new perspective about some aspects of the current research in Cosmology. We start with a brief introduction about the main developments of the field in the last century; then we introduce an analogy that shall elucidate…
An analysis of contemporary Cosmology is presented, with the aim of identifying the elements present in it according to the scientific program structure created by I. Lakatos. We look at some modern controversies from this point of view and…
In this paper the concept of a partial cone metric space is investigated, some continuity type theorems, and fixed point theorems of contractive mappings in this generalized setting are proved as well as some theorems related to topological…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire…