Related papers: Listening to Celestial Algebras
In this paper we revisit the concept of conformality in the sense of Gauss in the context of octonions and Clifford algebras. We extend a characterization of conformality in terms of a system of partial differential equations and…
Over the last decade, cosmological observations have attained a level of precision which allows for detailed comparison with theoretical predictions. In this paper, we briefly review some studies of the current and prospected constraints…
Observational Cosmology has indeed made very rapid progress in recent years. The ability to quantify the universe has largely improved due to observational constraints coming from structure formation Measurements of CMB anisotropy and, more…
We consider composition and division algebras over the real numbers: We note two r\^oles for the group $G_{2}$: as automorphism group of the octonions and as the isotropy group of a generic 3-form in 7 dimensions. We show why they are…
We present a class of general prolate and oblate spheroidal spacetimes for the description of cosmic structures in the Universe. They are exact geometries which represent, in an appropriated way, the imbedding of spheroidal matter-energy…
A nontrivial topology of the spatial section of the universe is an observable, which can be probed for all locally homogeneous and isotropic universes, without any assumption on the cosmological density parameters. We discuss how one can…
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…
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,…
This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…
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…
In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of…
String cosmology aims at providing a reliable description of the very early Universe in the regime where standard-model physics is no longer appropriate, and where we can safely apply the basic ingredients of superstring models such as…
In these lectures I review the present status of the so-called Standard Cosmological Model, based on the hot Big Bang Theory and the Inflationary Paradigm. I will make special emphasis on the recent developments in observational cosmology,…
Two strands of observational gravitation, one the search for astrophysical evidence of primordial black holes and the other the search for gravitational waves, may combine to provide strong evidence in favour of cosmological models based on…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
C*-algebras are widely used in mathematical physics to represent the observables of physical systems, and are sometimes taken as the starting point for rigorous formulations of quantum mechanics and classical statistical mechanics.…
Traditionally, collider experiments have been the primary tool used in searching for particle physics beyond the Standard Model. In this talk, I will discuss alternative approaches for exploring exotic physics scenarios using high energy…
The main tools in cosmology for comparing theoretical models with the observations of the galaxy distribution are statistical. We will review the applications of spatial statistics to the description of the large-scale structure of the…
This paper studies the restriction multiplicities of half-diagram modules for the partition algebra and their geometric interpretations. By specializing the Bowman-De Visscher-Orellana formula [BVC, Theorem 4.3] for restriction…
The current description of fundamental interactions is based on two theories with the status of standard models. The electromagnetic and nuclear interactions are described at a quantum level by the Standard Model of particle physics, using…