Higgs bundles introduction

Author: wxxh

August undefined, 2024

WebHiggs bundles were introduced by Hitchin [19] and are of interest for a variety of reasons. One is that they provide the framework for the generali-sation of the theorem of … Web5 de abr. de 2014 · In this chapter we give an introduction to Higgs bundles and their application to the study of surface group representations. This is based on two …

INTRODUCTION TO HIGGS BUNDLES - uni-hamburg.de

Web1 Introduction The aim of this article is to extend the Donaldson-Corlette-Hitchin-Simpson correspondence between Higgs bundles and flat connections on compact Kähler manifolds to the class of compact quasi-regular Sasakian manifolds. Web17 de abr. de 2024 · Higgs bundles were introduced by Hitchin [ 14] in his study of self-dual equations on a Riemann surface, and studied by Simpson [ 27] in his work on non-abelian Hodge theory. map of newmarket area

MSRI Workshop Schedules An introduction to Higgs bundles - I

WebHiggs Bundles Peter Gothen Centro de Matem´atica da Universidade do Porto International School on Geometry and Physics: moduli spaces in geometry, topology and physics. Ci … Web3 de jul. de 2024 · A Higgs bundle on a Riemann surface is a pair consisting of a holomorphic vector bundle together with an endomorphism valued holomorphic one-form, called the Higgs field. Taking the characteristic polynomial of the Higgs field defines the Hitchin map, which is a proper map from the moduli space of Higgs bundles to a vector … Web1 Introduction This paper studies the convergence properties of the gradient ﬂow of the Yang-Mills-Higgs functional on the space of Higgs bundles over a compact Riemann surface, as introduced by Hitchin in [10]. Higgs bundles that minimise this func-tional correspond to solutions of Hitchin’s self-duality equations, which (modulo map of newmilns ayrshire

(PDF) What is ⋯ a Higgs bundle? - ResearchGate

Surface group representations to 𝖲𝖫⁢(2,ℂ) and Higgs bundles ...

Webℓ-ADIC LOCAL SYSTEMS AND HIGGS BUNDLES 5 Theorem 1.2. Under the condition of the theorem 1.1, there are q-Weil integers αand integers mα such that Eirr n (R) Frob∗k = Pic0 X(Fqk) X α mαα k, ∀k> 1. The αthat appeared in the above equality are monomials in q-Weil numbers of the curve Xand roots of unity.Here q-Weil numbers of the curve Xrefer … WebWe show that for every nonelementary representation of a surface group into there is a Riemann surface structure such that the Higgs bundle associated to the representation lies outside the discriminant locus of the H… map of new mexico with interstateshttp://content.algebraicgeometry.nl/2024-3/2024-3-010.pdf kronos quartet house of the rising sun

"Web1 de dez. de 2013 · These objects are important because they provide a common generalization of several notions of bundles with structure; indeed principal bundles, … " - Higgs bundles introduction

Higgs bundles introduction

Stratifications on the nilpotent cone of the moduli space of Hitchin ...

WebarXiv:math/0610301v2 [math.AG] 12 Oct 2006 ALGEBRAIC NAHM TRANSFORM FOR PARABOLIC HIGGS BUNDLES ON P1 by Kurs¸at Aker¨ Feza Gursey Institute¨ Istanbul, Turkey & Szilard Szab´ WebA BRIEF SURVEY OF HIGGS BUNDLES 199 1 Introduction Nineteen years ago, the Clay Institute of Cambridge, Massachusets, presented seven millenium challenging problems. Yang-Mills and Mass Gap is one of those challenging unsolved problems. Newton’s classical mechanics laws stand

Did you know?

Web30 de set. de 2015 · The main purpose is to describe the new discovery of the relation between the following two disparate subjects: one is the topological recursion, that has its origin in random matrix theory and has been effectively applied to many enumerative geometry problems; and the other is the quantization of Hitchin spectral curves … WebHiggs bundles were introduced by Hitchin in [N1] as solutions of the so-called Hitchin equations, the 2-dimensional reduction of the Yang-Mills self-duality equations, given by where F A is the curvature of a unitary connection ∇A = ∂A + ¯¯ ¯∂A associated to the ¯¯ ¯∂ -connection ¯¯ ¯∂A on a principal GC bundle P .

WebAbstract. I will review the basic concepts of Higgs bundles and the moduli space of Higgs bundles, and then focus the non-Abelian Hodge correspondence: relation between the … WebIn this paper, we study the existence of Poisson metrics on flat vector bundles over noncompact Riemannian manifolds and discuss related consequence, specially on the applications in Higgs bundles, towards generalizing…

Web15 de set. de 2024 · An Introduction to Higgs Bundles via Harmonic Maps. These notes are an extended version of lecture notes prepared for the 3-hour mini-course "An … Web2.2 Moduli of Higgs bundles Usually one would start out with ordinary Higgs bundles, but with an eye to what will come later, we go straight to the parabolic case. Roughly this …

Web15 de set. de 2024 · An Introduction to Higgs Bundles via Harmonic Maps Qiongling Li This survey studies equivariant harmonic maps arising from Higgs bundles. We explain …

Webometry, Higgs bundles. Mathematical Subject Classiﬁcication 14G22, 14H60, 14F35 Contents 1. ... Introduction Inthecomplex case, Simpson correspondence generalizes theclassical Narasimhan- map of new mexico counties showing bordersHiggs bundles were first introduced by Hitchin in 1987, for the specific case where the holomorphic vector bundle E is over a compact Riemann surface. Further, Hitchin's paper mostly discusses the case where the vector bundle is rank 2 (that is, the fiber is a 2-dimensional vector space). The rank 2 … Ver mais In mathematics, a Higgs bundle is a pair $${\displaystyle (E,\varphi )}$$ consisting of a holomorphic vector bundle E and a Higgs field $${\displaystyle \varphi }$$, a holomorphic 1-form taking values in the bundle of … Ver mais • Hitchin system Ver mais kronos quartet at university of richmondWebHiggs bundles were introduced by Nigel Hitchin in 1987 while studying the dimensional reduction of the self-duality equations from four to two dimensions. A Higgs bundle on a Riemann surface is a pair (E;), where E is a holomorphic vector bundle and , the Higgs eld, is a holomorphic 1-form with values in the bundle of endomorphisms of E. It map of new mexico colorado borderWebbundles is in some sense bounded by the dimension of the manifold. This the-orem can be proved using some simple facts about homotopy and transversality of sections of vector … kronos punch locationWebThe non-abelian Hodge theory identifies moduli spaces of representations with moduli spaces of Higgs bundles through solutions to Hitchin's selfduality equations. On the one hand, ... We hope to give a gentle introduction to this theory, and to introduce some modern explorations along this theme. Turning smooth 4-manifolds into maps between ... map of new mexicaoWebHIGGS BUNDLES SOURAV DAS Abstract In a recent paper [3], a semi-stable degeneration of modulispace ofHiggs bundles on a curve has been constructed.Inthispaper,weshowthatthereisarelativelog-symplecticformonthisdegeneration,whose restriction to the generic ﬁbre is the classical … kronos punch in/outhttp://gear.math.illinois.edu/programs/workshops/documents/Bradlow-lecture1-slides.pdf map of new mexico highways and roads