Related papers: Stereotype Dualities in Geometry
This is an expository article, closely following the author's lecture at the 2014 Journal Differential Geometry conference.
Jacques Tits gave a general recipe for producing an abstract geometry from a semisimple algebraic group. This expository paper describes a uniform method for giving a concrete realization of Tits's geometry and works through several…
Profinite algebras are the residually finite compact algebras; their underlying topological spaces are Stone spaces. We extend the theory of profinite algebras to a more general setting of Stone topological algebras. We introduce Stone…
This is my talk at ICM, Zurich 1994. It contains a short introduction, two basic examples and a refined version of the Mirror Conjecture formulated in terms of homological algebra.
In this text, we outline a theory of schemes associated with a site, which generalizes a variety of geometries, such as manifolds, schemes, analytic spaces, simplicial complexes, and more. We present an abstract process of gluing model…
A class of mathematical dualities have played a central role in mapping states in gauge theory to states in the spacetime string theory dual. This includes the classical Schur-Weyl duality between symmetric groups and Unitary groups, as…
This review is devoted to some aspects of non-linear Supersymmetry in four dimensions that can be efficiently described via nilpotent superfields, in both rigid and curved Superspace. Our focus is mainly on the partial breaking of rigid…
The methods of Information geometry have been glowing up to develop various subjects of theoretical physics, including quantum information systems. The present article has two purposes. The first one is to develop general theory of…
Local symmetries is one of the most successful themes in modern theoretical physics. Although they are usually associated to Lie algebras, a gradual increase of interest in more general situations where local symmetries are associated to…
The geometry of (2,1) supersymmetric sigma-models is reviewed and the conditions under which they have isometry symmetries are analysed. Certain potentials are constructed that play an important role in the gauging of such symmetries. The…
This survey aims to provide a guide to the literature on topological 4-manifolds. Foundational theorems on 4-manifolds are stated, especially in the topological category. Precise references are given, with indications of the strategies…
We propose a novel type of duality that connects a sequence of well-known theories with even-multiplicity scalar amplitudes: it relates the Yang-Mills theory coupled to a specific scalar matter sector to the nonlinear sigma model on a…
We give an overview of results on irregular complex surfaces of general type, discussing in particular the distribution of the numerical invariants self-intersection of a canonical divisor and holomorphic Euler characteristic for the…
The dual complex associated to a resolution of singularities generalizes the notion of a resolution graph of a surface singularity to any dimension. We show that homotopy type of the dual complex is an invariant of an isolated singularity.
This work deals with the notion of Newton complementary duality as raised originally in the work of the second author and B. Costa. A conceptual revision of the main steps of the notion is accomplished which then leads to a vast…
This book is a course in Stone-Priestley duality theory, with applications to logic and theoretical computer science. Our target audience are graduate students and researchers in mathematics and computer science. Our aim is to get in a…
We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed…
In this letter we implement a recently proposed {\it spacetime duality} approach to dualize a two dimensional, Abelian, gauge field theory, which has no dual version under $p$--duality. Our result suggests that spacetime duality spans a…
This report on the topics in the title was written for a lecture series at the Southwestern Center for Arithmetic Algebraic Geometry at the University of Arizona.It may serve as an introduction to certain conjectural relations between…
This is an expository article for Elsevier's Encyclopedia of Mathematical Physics on the subject in the title. Comments/corrections welcome.