Related papers: Cosmology of Plane Geometry
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
In this article first we present a brief review of some alternative theories of cosmology. Then by referring to some of the main works done in these theories we show that how they can describe the phenomena which are explained nowadays in…
The main purpose of this paper is to present a new approach to logic or what we will call superlogic. This approach constitutes a new way of looking at the connection between quantum mechanics and logic. It is a {\it geometrisation} of the…
We consider an extension of Weyl geometry with the most general connection linearly determined by a vector field. We discuss some of the geometrical properties within this framework and then we construct gravitational theories leading to an…
The new classes of homogeneous cosmological models for the scalar fields are build in the context of Lyra's geometry. The different types of exact solution for the model are obtained by applying two procedures, viz the generating function…
This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical…
By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are…
Cosmography is the tool that makes possible to untie the interpretation of cosmological observations from the definition of any dynamical prior. We review the constraints on the cosmographic parameter obtained using the most thorough data…
We have a well-established standard model for cosmology and prospects for considerable additions from work in progress. I offer a list of elements of the standard model, comments on controversies in the interpretation of the evidence in…
The research field of spatial scientometrics is dedicated to measuring and analyzing science with spatial components (e.g., location, place, mapping). Because of the dynamic nature of this field, researchers from multidisciplinary domains…
In this paper we focus on various aspects of singular complex plane curves, mostly in the context of their homological properties and the associated combinatorial structures. We formulate some challenging open problems that can point to new…
This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in which rational homogeneous spaces play a prominent r{\^o}le. This selection is largely…
This is a broad and in places unconventional overview of the strengths and shortcomings of our standard models of fundamental physics and of cosmology. The emphasis is on ideas that have accessible experimental consequences. It becomes…
We study the geometry of spaces of planes on smooth complete intersections of three quadrics, with a view toward rationality questions.
This article studies the possible degenerations of plane Cremona transformations of some degree into maps of smaller degree.
This paper examines the concept of gluing, placing it within its most general categorical context and tracing its foundational role in the broader architecture of algebraic geometry.
This paper shows how a recent reformulation of the basics of classical geometry and trigonometry reveals a three-fold symmetry between Euclidean and non-Euclidean (relativistic) planar geometries. We apply this chromogeometry to look at…
Some aspects of Cosmology with primordial black holes are briefly reviewed
This paper is about Information Geometry, a relatively new subject within mathematical statistics that attempts to study the problem of inference by using tools from modern differential geometry. This paper provides an overview of some of…
This contribution presents the cosmological models with extra dimensions that have been recently elaborated, which assume that ordinary matter is confined on a surface, called brane, embedded in a higher dimensional spacetime.