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Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…

We present an algorithm that enumerates and classifies all edge-to-edge gluings of unit squares that correspond to convex polyhedra. We show that the number of such gluings of $n$ squares is polynomial in $n$, and the algorithm runs in time…

We show how Coxeter's work implies a bijection between complex reflection groups of rank two and real reflection groups in $O(3)$. We also consider this magic square of reflections and rotations in the framework of Clifford algebras: we…

We define certain natural finite sums of $n$'th roots of unity, called $G_P(n)$, that are associated to each convex integer polytope $P$, and which generalize the classical $1$-dimensional Gauss sum $G(n)$ defined over $\mathbb Z/ {n…

We describe a new sequence of polytopes which characterize A_infinity maps from a topological monoid to an A_infinity space. Therefore each of these polytopes is a quotient of the corresponding multiplihedron. Later term(s) in our sequence…

In the present paper we address the interaction of pairs of charmed mesons with hidden charm in a finite box. We use the interaction from a recent model based on heavy quark spin symmetry that predicts molecules of hidden charm in the…

In this work, we find novel static and spherically symmetric wormhole geometries using a three-form field. By solving the gravitational field equations, we find a variety of analytical and numerical solutions and show that it is possible…

This article looks at the eigenvalues of magic squares generated by the MATLAB's magic($n$) function. The magic($n$) function constructs doubly even ($n = 4k$) magic squares, singly even ($n = 4k+2$) magic squares and odd ($n = 2k+1$) magic…

Multipolar expansions are a foundational tool for describing basis functions in quantum mechanics, many-body polarization, and other distributions on the unit sphere. Progress on these topics is often held back by complicated and competing…

We deduce the appearance of a polymeric phase in 4-dimensional simplicial quantum gravity by varying the values of the coupling constants and discuss the geometric structure of the phase in terms of ergodic moves. A similar result is true…

We propose a geometric framework where dispersion relations are viewed as parametric surfaces in energy-momentum space. Within this picture, the presence and type of critical points of the surface emerge as clear geometric signatures of…

It is evident that the positions of 4 bodies in $d>2$ dimensional space can be identified with vertices of a tetrahedron. Square of volume of the tetrahedron, weighted sum of squared areas of four facets and weighted sum of squared edges…

We discuss the geometry of dynamical triangulations associated with 3-dimensional and 4-dimensional simplicial quantum gravity. We provide analytical expressions for the canonical partition function in both cases, and study its large volume…

The macroscopic entropy-area formula for supersymmetric black holes in N=2,4,8 theories is found to be universal: in d=4 it is always given by the square of the largest of the central charges extremized in the moduli space. The proof of…

We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…

We show by explicit construction the existence of various four dimensional models of type II superstrings with N=2 supersymmetry, purely vector multiplet spectrum and no hypermultiplets. Among these, two are of special interest, at the…

This note includes results of a study of stationary spherically symmetric ``dark holes'', objects merging central black holes and peripheral scalar graviton dark haloes arising in the framework of the modified gravity -- the quartet-metric,…

Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…

This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…

The phase space of general relativity in a finite subregion is characterized by edge modes localized at the codimension-2 boundary, transforming under an infinite-dimensional group of symmetries. The quantization of this symmetry algebra is…