Related papers: Non-Abelian Stokes Theorem
In this paper, two parallel notions of convexity of sets are introduced in the abelian semigroup setting. The connection of these notions to algebraic and to set-theoretic operations is investigated. A formula for the computation of the…
These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone…
We exploit a new theory of duality transformations to construct dual representations of models incompatible with traditional duality transformations. Hence we obtain a solution to the long-standing problem of non-Abelian dualities that…
In this article we establish some formalism of Derived Witt-D\'evissage theory for resolving subcategories of abelian categories. Results directly apply to noetherian schemes.
This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.
In this paper we define a notion of gerbed tower, and use this notion to give a geometric representation of cohomological classes.
The note introduces a novel concept of non-Abelian patchworking arising as real locus of non-Abelian complex-phase tropical hypersurfaces, the theory of which is now developed enough to allow the proposed spin-off. Although, non-Abelian…
This is a chapter of an encyclopedia which does not have an abstract.
This is a survey of noncommutative generalizations of the spectrum of a ring, written for the Notices of the American Mathematical Society.
We revisit Ahlfors theory of covering surfaces thanks to Stokes theorem.
This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also…
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
In this chapter, we report the recent progress in the understanding of the rich mathematical structures of topological insulators in the framework of index theory and noncommutative geometry.
This paper settles the question of injectivity of the non-Abelian X-ray transform on simple surfaces for the general linear group of invertible complex matrices. The main idea is to use a factorization theorem for Loop Groups to reduce to…
This manuscript has been withdrawn by the author. Some of the material has been included in the manuscript 'Embedded Monopoles' at hep-th/0106254.
We survey recent advances in non-abelian Hodge theory in the "mixed" setting of non-proper algebraic varieties. We then describe how these tools are used to construct algebraic Shafarevich morphisms and prove a version of the linear…
This is a series of lecture notes, with embedded problems, aimed at students studying differential topology. Many revered texts, such as Spivak's "Calculus on Manifolds" and Guillemin and Pollack's "Differential Topology" introduce forms by…
We study toroidal orbifold models with topologically invariant terms in the path integral formalism and give physical interpretations of the terms from an operator formalism point of view. We briefly discuss a possibility of a new class of…
We prove a noncommutative version of Bishop's peak interpolation-set theorem.
This extended preface [to the Book `Bayesian Nonparametrics', Cambridge University Press, 2010, by NL Hjort, CC Holmes, P Mueller, SG Walker] is meant to explain why you are right to be curious about Bayesian nonparametrics -- why you may…