Vector bundles | Complex manifolds

Higgs bundle

In mathematics, a Higgs bundle is a pair consisting of a holomorphic vector bundle E and a Higgs field , a holomorphic 1-form taking values in the bundle of endomorphisms of E such that . Such pairs were introduced by Nigel Hitchin, who named the field after Peter Higgs because of an analogy with Higgs bosons. The term 'Higgs bundle', and the condition (which is vacuous in Hitchin's original set-up on Riemann surfaces) was introduced later by Carlos Simpson. A Higgs bundle can be thought of as a "simplified version" of a flat holomorphic connection on a holomorphic vector bundle, where the derivative is scaled to zero. The nonabelian Hodge correspondence says that, under suitable stability conditions, the category of flat holomorphic connections on a smooth, projective complex algebraic variety, the category of representations of the fundamental group of the variety, and the category of Higgs bundles over this variety are actually equivalent. Therefore, one can deduce results about gauge theory with flat connections by working with the simpler Higgs bundles. (Wikipedia).

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An introduction to spectral data for Higgs bundles.. by Laura Schaposnik

Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio

From playlist Higgs Bundles

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An introduction to spectral data for Higgs bundles.. by Laura Schaposnik

Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio

From playlist Higgs Bundles

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An introduction to spectral data for Higgs bundles.. by Laura Schaposnik

Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio

From playlist Higgs Bundles

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An introduction to spectral data for Higgs bundles.. by Laura Schaposnik

Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio

From playlist Higgs Bundles

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Jørgen Ellegaard Andersen: The Verlinde formula for Higgs bundles

Abstract: In this talk we will present a Verlinde formula for the quantization of the Higgs bundle moduli spaces and stacks for any simple and simply-connected group. We further present a Verlinde formula for the quantization of parabolic Higgs bundle moduli spaces and stacks. We will expl

From playlist Mathematical Physics

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Nigel Hitchin "Higgs bundles, past and present" [2012]

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From playlist Number Theory

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Holomorphic rigid geometric structures on compact manifolds by Sorin Dumitrescu

Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio

From playlist Higgs Bundles

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The Weil-Petersson current for moduli of vector bundles and... by Schumacher

Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio

From playlist Higgs Bundles

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Equivariant principal bundle over toric variety by Arijit Dey

Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio

From playlist Higgs Bundles

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Steven Bradlow - Exotic components of surface group representation varieties

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From playlist Maryland Analysis and Geometry Atelier

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Conformal Limits of Parabolic Higgs Bundles by Richard Wentworth

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From playlist Vortex Moduli - 2023

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Higgs bundles, harmonic maps, and applications by Richard Wentworth

Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio

From playlist Higgs Bundles

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Higgs Bundles and Higher Teichmüller Spaces - Brian Collier

Glimpses of Mathematics, Now and Then: A Celebration of Karen Uhlenbeck's 80th Birthday Topic: Higgs Bundles and Higher Teichmüller spaces Speaker: Brian Collier Affiliation: University of California, Riverside Date: September 17, 2022 The Teichm\"uller space of a compact surface S is re

From playlist Glimpses of Mathematics, Now and Then: A Celebration of Karen Uhlenbeck's 80th Birthday

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Higgs bundles and higher Teichmüller components (Lecture 1) by Oscar Garcia

DISCUSSION MEETING : MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE : 10 February 2020 to 14 February 2020 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classif

From playlist Moduli Of Bundles And Related Structures 2020

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Minimal Surfaces in $CH^2$ and their Higgs Bundles by John Loftin

Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio

From playlist Higgs Bundles

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Higgs bundles, harmonic maps, and applications by Richard Wentworth

Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio

From playlist Higgs Bundles

Related pages

Nonabelian Hodge correspondence | Hitchin system | Fundamental group | Riemann surface | Kähler manifold | Principal bundle | Holomorphic vector bundle | Mathematics | Hitchin's equations | Projective variety | Affine connection | Category (mathematics)