Higgs bundles introduction

Author: iwon

August undefined, 2024

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… 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 …

Semistable Higgs Bundles Over Compact Gauduchon Manifolds

WebAn Introduction to Higgs Bundles via Harmonic Maps 3 notions can be de ned for higher-dimensional manifolds. But for simplicity, we only deal with surfaces and one may notice … WebMini course 2: Introduction to Higgs bundles (Lecture - 1) by Francois Labourie - YouTube Geometry, Groups and Dynamics (GGD) - 2024DATE: 06 November 2024 to 24 November 2024VENUE: Ramanujan... chris dawson new evidence

Laura P. Schaposnik Department of Mathematics University of …

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 … WebAn Introduction to Higgs Bundles via Harmonic Maps Qiongling Li Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China Received October 16, … WebHiggs 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 … chris dawson marriage counsellor

Hilbert Schemes as Moduli of Higgs Bundles and Local Systems

HIGGS BUNDLES AND LOCAL SYSTEMS ON RIEMANN SURFACES

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. 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… chris dawson new chargesWebHiggs 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 . genthe glas goslar

"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 … " - Higgs bundles introduction

Higgs bundles introduction

15 (2024), 035, 30 pages An Introduction to Higgs Bundles via

WebHoje · Abstract. We are interested in studying the variation of the Hitchin fibration in moduli spaces of parabolic Higgs bundles, under the action of a ramified covering. Given a degree two map π: Y → X between compact Riemann surfaces, we may pull back a Higgs bundle from X to Y, the lifted Higgs bundle tends to have many apparent singularities ... Webthe School’s four lecture series was to give a rapid introduction to Higgs bundles, representation varieties, and mathematical physics. While the scope of these subjects is …

Did you know?

WebThis paper is an introduction to the Higgs bundle theory of Hitchin and Simpson and its applications to the study of representations of complex hyperbolic lattices ... Higgs bundles and representations of complex hyperbolic lattices 3 and not locally isomorphic to PSL(2;R) are uniquely determined by .

WebHiggs 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 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

Webbundles 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 … Web27 de ago. de 2024 · The aim is to provide a brief introduction to algebraic stacks, and then to give several constructions of the moduli stack of Higgs bundles on algebraic curves. …

WebCoHA of Higgs sheaves on a curve system, called the Hitchin bration. The preimage with respect to zero of the Hitchin bration is the so-called global nilpotent cone, which parameterizes stable Higgs bundles (F;˚) with nilpotent Higgs eld ˚. Since its introduction, the Hitchin moduli space has played a pre-eminent role in

Web27 de ago. de 2024 · The aim is to provide a brief introduction to algebraic stacks, and then to give several constructions of the moduli stack of Higgs bundles on algebraic curves. The first construction is via a "bootstrap" method from the algebraic stack of vector bundles on an algebraic curve. genthe glas agWebHiggs Bundles - Yale University chris dawson orenda real estatehttp://content.algebraicgeometry.nl/2024-3/2024-3-010.pdf genthe goslarHiggs 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 chris dawson painter decoratorWebarXiv: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´ gen the hedgehogWeb1 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. genthe honda partsWebWhat are Higgs bundles? How do they relate to surface group representations? What do we gain by taking the Higgs bundle point of view? The Plan: 1 (Lectures I and … chris dawson jcw