Related papers: Cosmology of Plane Geometry
This mini-review provides a perspective on recent progress and emerging directions aimed at utilizing and controlling in-plane optical polarization, highlighting key application spaces where in-plane near-field tip responses have enabled…
Many different and complementary strategies for translating the basic principle of multiple topological imaging into observational analysis are now available, both for three-dimensional and two-dimensional catalogues.
Cosmology differs in some respects significantly from other sciences, primarily because of its intimate association with issues of a conceptual and philosophical nature. Because cosmology in the broader sense relates to the world views held…
Cosmography represents an important branch of cosmology which aims to describe the universe without the need of postulating \emph{a priori} any particular cosmological model. All quantities of interest are expanded as a Taylor series around…
I review the reason for considering the prime purpose of the program of measurements of the fundamental parameters of cosmology to be the tests of cosmological models. I comment on the philosophy by which we are approaching this goal, offer…
Questions such as whether we live in a spatially finite universe, and what its shape and size may be, are among the fundamental open problems that high precision modern cosmology needs to resolve. These questions go beyond the scope of…
An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, spinor and twistor methods, heaven…
In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.
Revolutionary advances in both theory and technology have launched cosmology into its most exciting period of discovery yet. Unanticipated components of the universe have been identified, promising ideas for understanding the basic features…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
An introductory guide to mathematical cosmology is given focusing on the issue of the genericity of various important results which have been obtained during the last thirty or so years. Some of the unsolved problems along with certain new…
This paper introduces a notion of generalised geometric logic. Connections of generalised geometric logic with L-topological system and L-topological space are established.
We review some aspects of quantum gravity in the context of cosmology. In particular, we focus on models with a phenomenology accessible to current and near-future observations, as the early Universe might be our only chance to peep through…
Making a survey of recent constructions of universal cohomologies we suggest a new framework for a theory of motives in algebraic geometry.
This is a series of lectures on M Theory for cosmologists. After summarizing some of the main properties of M Theory and its dualities I show how it can be used to address various fundamental and phenomenological issues in cosmology.
The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize themselves with PGA. After a brief…
We present an elementary account of mathematical cosmology through a series of important unsolved problems. We introduce the fundamental notion of `a cosmology' and focus on the issue of singularities as a theme unifying many current,…
The recently unveiled deep-field images from the James Webb Space Telescope have renewed interest in what we can and cannot see of the universe. Answering these questions requires understanding the so-called "cosmological horizons" and the…
An old branch of mathematics, Topology, has opened the road to the discovery of new phases of matter. A hidden topology in the energy spectrum is the key for novel conducting/insulating properties of topological matter.
We discuss a number of fundamental aspects of modern cosmological concepts, from the phenomenological, observational, theoretical and epistemic points of view. We argue that the modern cosmology, despite a great advent, in particular in the…