Related papers: Supergeometry in mathematics and physics
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
This work is a continuation of [1]. As in the previous article, here we will describe some interesting ideas and a lot of new theorems in plane geometry related to them.
We investigate a special kind of contraction of symmetric spaces (respectively, of Lie triple systems), called homotopy. In this first part of a series of two papers we construct such contractions for classical symmetric spaces in an…
We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and…
A superfield formalism for quantum fields with N-extended superconformal symmetry is developed using vertex algebra techniques in four dimensions.
A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…
This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in which rational homogeneous spaces play a prominent r{\^o}le. This selection is largely…
This is the first chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.
A speculative discussion on the role of various symmetries in physics.
Whereas for a substantial part, Finite Geometry during the past 50 years has focussed on geometries over finite fields, geometries over finite rings that are not division rings have got less attention. Nevertheless, several important…
This article is an interdisciplinary review and an on-going progress report over the last few years made by myself and collaborators in certain fundamental subjects on two major theoretic branches in mathematics and theoretical physics:…
This text serves as an introduction to $\mathbb{F}_1$-geometry for the general mathematician. We explain the initial motivations for $\mathbb{F}_1$-geometry in detail, provide an overview of the different approaches to $\mathbb{F}_1$ and…
Huang's geometric interpretation of vertex operator algebras is extended to a supergeometric interpretation of vertex operator superalgebras. In particular, the geometry of spheres with punctures and local analytic coordinates in terms of…
A recollection of some theoretical developments that preceded and followed the first formulation of supergravity theory is presented. Special emphasis is placed on the impact of supergravity on the search for a unified theory of fundamental…
The role mathematics plays within physics has been of sustained interest for physicists as well as for philosophers and historians of science. We explore this topic by tracing the role the mathematical structure associated with SU(2) has…
See math.CV/0509030 which replaces this paper.
We discuss the issue of motivating the analysis of higher order gravity theories and their cosmologies and introduce a rule which states that these theories may be considered as a vehicle for testing whether certain properties may be of…
One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…
The geometry of jets of submanifolds is studied, with special interest in the relationship with the calculus of variations. A new intrinsic geometric formulation of the variational problem on jets of submanifolds is given. Working examples…