Related papers: Cosmic crystallography: the hyperbolic isometries
This is an expository essay about systolic geometry. It describes a central theorem in the subject and why the proof is difficult. Then it discusses different metaphors which suggest ways to approach the problem. The metaphors connect the…
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
This is the first in a series of three papers describing a project with the Cosmic Origins Spectrograph on the Hubble Space Telescope to measure abundances of the neutral interstellar medium (ISM) in a sample of 9 nearby star-forming…
The spatial arrangement of galaxies (of satellites on a scale of 100kpc) as well as their three-dimensional distribution in galaxy groups such as the Local Group (on a scale of 1Mpc), the distribution of galaxies in the nearby volume of…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
Hyperbolic geometry, a Riemannian manifold endowed with constant sectional negative curvature, has been considered an alternative embedding space in many learning scenarios, \eg, natural language processing, graph learning, \etc, as a…
On the basis of the relativistic kinetic theory the relativistic statistical systems with scalar interaction particles are investigated. The self-consistent system of the equations describing self-gravitating plasma with interpartial scalar…
Cosmic structure simulations have improved enormously over the past decade, both in terms of the resolution which can be achieved, and with the addition of hydrodynamic and other techniques to formerly purely gravitational methods. This is…
We demonstrate the quasi-isometry invariance of two important geometric structures for relatively hyperbolic groups: the coned space and the cusped space. As applications, we produce a JSJ-decomposition for relatively hyperbolic groups…
Observational Cosmology has indeed made very rapid progress in the past decade. The ability to quantify the universe has largely improved due to observational constraints coming from structure formation Measurements of CMB anisotropy and,…
The main goal of this note is to show that the study of closed hyperbolic surfaces with maximum length systole is in fact the study of surfaces with maximum length homological systole. The same result is shown to be true for once-punctured…
We study the phase space of spatially homogeneous and isotropic cosmology in general scalar-tensor theories. A reduction to a two-dimensional phase space is performed when possible-in these situations the phase space is usually a…
We use cosmography to present constraints on the kinematics of the Universe, without postulating any underlying theoretical model. To this end, we use a Monte Carlo Markov Chain analysis to perform comparisons to the supernova Ia Union 2…
Higher dimensional solutions are obtained for a homogeneous, spatially isotropic cosmological model in Wesson theory of gravitation. Some cosmological parameter are also calculated for this model.
Aim of this paper is to review some basic ideas and recent developments in the theory of strictly hyperbolic systems of conservation laws in one space dimension. The main focus will be on the uniqueness and stability of entropy weak…
The large-scale distribution of matter, as mapped by photometric surveys like the Dark Energy Survey (DES), serves as a powerful probe into cosmology. It is especially sensitive to both the amplitude of matter clustering ($\sigma_8$) and…
We present new calculations of the inhomogeneous process of cosmological reionization by carefully following the radiative transfer in pre-computed hydrodynamical simulations of galaxy formation. These new computations represent an…
We consider families of B\"or\"oczky tilings in hyperbolic space in arbitrary dimension, study some basic properties and classify all possible symmetries. In particular, it is shown that these tilings are non-crystallographic, and that…
In this talk, I review some recent work on cosmic microwave background (CMB) anisotropies in an open universe. I emphasize that the observed CMB anisotropies are still consistent with a low value of $\Omega$, and I address the question of…
A mathematical model of the cosmological evolution of statistical systems of scalarly charged particles with Higgs scalar interaction is formulated and investigated. Examples are given of numerical modeling of such systems, revealing their…