Related papers: Matrix Geometries Emergent from a Point
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
This paper exposes the language of geometric contexts and elementary schemes, which is a functorial formalism to study categories of geometric objects such as schemes, topological manifolds, differential manifolds, analytic manifolds, etc.…
The purpose of this note is to show that W3 algebras originate from an unusual interplay between the breakings of the reparametrization invariance under the diffemorphism action on the cotangent bundle of a Riemann surface. It is recalled…
Any procedure applied to data, and any quantity derived from data, is required to respect the nature and symmetries of the data. This axiom applies to refinement procedures and multiresolution transforms as well as to more basic operations…
In a recent paper, an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices -- the so called `matrix properties'. In this paper we extend this algorithm to…
In this paper, we extend the notion of orthogonality to the general elements of an absolute matrix order unit space and relate it to the orthogonality among positive elements. We introduce the notion of a partial isometry in an absolute…
We characterize mutation-finite cluster algebras of rank at least 3 using positive semi-definite quadratic forms. In particular, we associate with every unpunctured bordered surface a positive semi-definite quadratic space $V$, and with…
Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
We present a new multitrace matrix model, which is a generalization of the real quartic one matrix model, exhibiting dynamical emergence of a fuzzy two-sphere and its non-commutative gauge theory. This provides a novel and a much simpler…
We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings,…
The purpose of this article is to introduce projective geometry over composition algebras : the equivalent of projective spaces and Grassmannians over them are defined. It will follow from this definition that the projective spaces are in…
The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…
This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…
In this paper, we establish a general setup for studying incidence-preserving motions of projective geometric configurations of points and lines via a "projective rigidity matrix". The spaces of infinitesimal motions of a point-line…
A geometric approach to understanding recursion relations for scattering amplitudes is developed. We achieve this by studying intersection numbers of triangulated accordiohedra presented as hyperplane arrangements. The cancellation of…
Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…
One considers certain degenerations of the generic symmetric matrix over a field $k$ of characteristic zero and the main structures related to the determinant $f$ of the matrix, such as the ideal generated by its partial derivatives, the…
Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…
The domains of mesh functions are strict subsets of the underlying space of continuous independent variables. Spaces of partial maps between topological spaces admit topologies which do not depend on any metric. Such topologies…