Related papers: Hyperbolic and Circular Trigonometry and Applicati…
General relativity can describe various gravitational systems of astrophysical relevance, like black holes and neutron stars, or even strongly coupled systems through the holographic duality. The characteristic initial (boundary) value…
We introduce hyperbolic attention networks to endow neural networks with enough capacity to match the complexity of data with hierarchical and power-law structure. A few recent approaches have successfully demonstrated the benefits of…
Elements of supergeometry are an ingredient in many contemporary classical and quantum field models involving odd fields. For instance, this is the case of SUSY field theory, BRST theory, supergravity. Addressing to theoreticians, these…
We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large…
This survey introduces to the hyperbolic unfolding correspondence that links the geometric analysis of minimal hypersurfaces with that of Gromov hyperbolic spaces. Problems caused from hypersurface singularities oftentimes become solvable…
The mathematical treatment and graphical representation of Special Relativity (SR) are well established, yet carry deep implications that remain hard to visualize. This paper presents a new graphical interpretation of the geometry of SR…
A modern elementary introduction to special relativity for advanced school children or first-year university students, in Russian. I try to demonstrate that relativity does not contradict common sense; on the contrary, it follows from…
In this paper, we intend to bring together the hyperbolic spinors, which are useful frameworks from mathematics to physics, and both spacelike and timelike framed curves in Minkowski 3-space $\mathbb{R}_1^3$, which are new type attractive…
The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…
Non-perturbative quantum general relativity provides a possible framework to analyze issues related to black hole thermodynamics from a fundamental perspective. A pedagogical account of the recent developments in this area is given. The…
In this paper we study the difference between algebraic and geometric solutions of the hyperbolic Dehn filling equations for ideally triangulated 3-manifolds. We show that any geometric solution is an algebraic one, and we prove the…
Using spacetime algebra, the geometric algebra of spacetime, the general problem of relativistic addition of velocities is addressed. The successive application of non-collinear Lorentz boosts is then studied in Minkowski spacetime. Even…
The principles of the special theory of relativity are extremely simple. A knowledge of the Pythagorean theorem and an ability to perform the simplest algebraic operations are sufficient to be conversant with the kinematics of the special…
Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…
We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries. In this transitional setting, several geometric…
In this paper we characterize hyperbolic geometry among Hilbert geometry by the property that three medians of any hyperbolic triangle all pass through one point.
The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…
Let N be a topologically finite, orientable 3-manifold with ideal triangulation. We show that if there is a solution to the hyperbolic gluing equations, then all edges in the triangulation are essential. This result is extended to a…
We present a large scale hyperbolic recommender system. We discuss why hyperbolic geometry is a more suitable underlying geometry for many recommendation systems and cover the fundamental milestones and insights that we have gained from its…