Related papers: Supergeometry in mathematics and physics
This is a review of concepts of noncommutative supergeometry - namely Hilbert superspace, C*-superalgebra, quantum supergroup - and corresponding results. In particular, we present applications of noncommutative supergeometry in harmonic…
The concept of torsion in geometry, although known for a long time, has not gained considerable attention by the physics community until relatively recently, due to its diverse and potentially important applications to a plethora of…
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…
The classifying space of inertial reference frames in special relativity is naturally hyperbolic. There is a remarkable interplay between central elements of hyperbolic geometry and those of special relativity -- which, to a certain extent,…
Supersymmetry phenomenology is an important component of particle physics today. I provide a definition of supersymmetry phenomenology, outline the scope of its activity, and argue its legitimacy. This essay derives from a presentation…
In this chapter we describe a selection of mathematical techniques and results that suggest interesting links between the theory of gratings and the theory of homogenization, including a brief introduction to the latter. By no means do we…
This survey focuses on the computational complexity of some of the fundamental decision problems in 3-manifold theory. The article discusses the wide variety of tools that are used to tackle these problems, including normal and almost…
Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance…
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…
In this review, we give a pedagogical introduction to a systematic framework for constructing and analyzing supersymmetric field theories on curved spacetime manifolds. The framework is based on the use of off-shell supergravity background…
This paper is an attempt to apply the tools of supergeometry to arithmetic. Supergeometric objects are defined over supercommutative rings of coefficients, and we consider an integral ring with exactly two odd variables. In this case the…
In this article we study the notion of supermanifolds families, starting from Green's general classification of supermanifolds. The topics studied divide this article into two distinct parts, labelled I and II respectively. Part I concerns…
We consider various $A_{\infty}$-algebras of differential (super)forms, which are related to gauge theories and demonstrate explicitly how certain reformulations of gauge theories lead to the transfer of the corresponding…
In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics, we briefly survey some peculiarities of geometric techniques in quantum models.
Parametric geometry of numbers is a new theory, recently created by Schmidt and Summerer, which unifies and simplifies many aspects of classical Diophantine approximations, providing a handle on problems which previously seemed out of…
Modular forms appear in many facets of mathematics, and have played important roles in geometry, mathematical physics, number theory, representation theory, topology, and other areas. Around 1994, motivated by technical issues in homotopy…
By systematically applying ten well-known and inequivalent two-part relations between hypergeometric sums 3F2(...|1) to the published database of all such sums, 62 new sums are obtained. The existing literature is summarized, and many…
Work in progress concerning alternative formalizations of arithmetic.
These notes aim at providing a complete and systematic account of some foundational aspects of algebraic supergeometry, namely, the extension to the geometry of superschemes of many classical notions, techniques and results that make up the…
The half-maximal supergravity theories in three dimensions, which have local $SO(8)\xz SO(n)$ and rigid SO(8,n) symmetries, are discussed in a superspace setting starting from the superconformal theory. The on-shell theory is obtained by…