Related papers: Revealing how different spinors can be: the Lounes…

In this article we are interested in a differential inclusion defined by an isotropic compact set.

This work is an introduction to the local geometric theory of Veronese webs developed in the last twenty years. Among the different possible approach, here one has chosen the point of view of differential forms. Moreover, in order to make…

Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures…

The goal of this paper is to define fermionic fields on causal set. This is done by the use of holonomies to define vierbines, and then defining spinor fields by taking advantage of the leftover degrees of freedom of holonomies plus…

A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.

Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is…

This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.

We prove a conjecture of Crapo and Penne which characterizes isotopy classes of skew configurations with spindle-structure. We use this result in order to define an invariant, spindle-genus, for spindle-configurations. We also slightly…

In this paper, we study the Lusternik-Schnirelmann category of a simplicial map between simplicial complexes, generalizing the simplicial category of a complex to that of a map. Several properties of this new invariant are shown, including…

In this paper, we perform the polar analysis of the spinorial fields, starting from the regular cases and up to the singular cases: we will give for the first time the polar form of the spinorial field equations for the singular cases…

In this paper we study the classification problem of convex lattice ploytopes with respect to given volume or given cardinality.

The present work consists of three parts. In the first one we determine the prototypes of separable Rosenthal compacta and we provide a classification theorem. The second part concerns an extension of a theorem of S. Todorcevic. The last…

In a series of recent papers, we have introduced an object that was constructed on the connection but which was proven to be a tensor: this object, thus called tensorial connection, has been defined and some of its properties have been…

The questions of the existence, basic algebraic properties and relevant constraints that yield a viable physical interpretation of world spinors are discussed in details. Relations between spinorial wave equations that transform…

We give an argument that a broad class of geometric models of spinning relativistic particles with Casimir mass and spin being separately fixed parameters, have indeterminate worldline (while other spinning particles have definite…

Some facts of the theory of the Lorentz group are specified for looking at the problems of light polarization optics in the frames of vector Stokes-Mueller and spinor Jones formalism. In view of great differences between properties of…

We explore new aspects of internal fermionic shifting symmetries, present in physical systems such as free Dirac spinors and p-form tensor-spinor fields. We propose a novel procedure to gauge these global symmetries, which also introduces a…

This focused issue attempts to provide a comprehensive introduction into the field of antiferromagnetic spintronics. Apart from the brief overview below, it features five review articles. The intention is to cover in a coherent and…

In this article, we firstly introduce higher spin Clifford analysis, which are considered as generalizations of classical Clifford analysis by considering functions taking values in irreducible representations of the spin group. Then, we…

In this paper we summarise the work discussed in Ref. [1] and [2] (q-alg/9505003), in which we introduced a method helpful in solving the problem of knot classification. We also present results obtained since then.