[Todos CMAT] Fwd: Minicurso fibrados de Higgs

[apasseggi en cmat.edu.uy]

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De: "Andrés Sambarino" 
Para: campi en fisica.edu.uy (mailto:campi en fisica.edu.uy), miguel en fisica.edu.uy (mailto:miguel en fisica.edu.uy), "Rafael Potrie" , apasseggi en cmat.edu.uy (mailto:apasseggi en cmat.edu.uy), miguel.campiglia en gmail.com (mailto:miguel.campiglia en gmail.com), "Miguel Paternain" , todos_imerl en fing.edu.uy (mailto:todos_imerl en fing.edu.uy)
Enviado: 12 de marzo del 2016 14:51
Asunto: Minicurso fibrados de Higgs
Buenas,
 En el marco de la escuela CIMPA 'Hyperbolic groups and representations (https://cimpapiriapolisuy.wordpress.com/)' y el Workshop 'Geometry of Groups (https://geometryandgroupsinmontevideo.wordpress.com/)', François Labourie (Profesor en Université Nice Sophia Antipolis) pasará un mes en Montevideo.
 Durante la semana del 18 al 22 de abril dictará un minicurso de 4h introductorio a los fibrados de Higgs. Abajo va un resumen general y una breve explicación de cada una de las 4 charlas.

Aquellos interesados escribanme (andres.sambarino en gmail.com (mailto:andres.sambarino en gmail.com)) con restriccion de horarios.
Salute

This mini course will give an introduction to the major results of the theory of Higgs bundles initiated by Kevin Corlette, Simon Donaldson, Nigel Hitchin and Carlos Simpson in the 90's. This theory is usually described as a non linear analogue of the classical hodge theory on Riemann surfaces which gives isomorphism a between various notions of cohomology: Dolbaut, de Rham, simplicial.

The mini course will consist in 4 lectures with little prerequisite and available online hand written notes.

The first lecture will describe background on semi simple groups and symmetric spaces.

The second lecture will describe harmonic mappings into symmetric spaces and Higgs bundles.

The third lecture will describe the three major constructions of the theory: the Hitchin-Simpson theorem, the Corlette-Donaldson theorem and the Hitchin Fibration which provides isomorphisms between natural generalizations of the cohomology theories for Riemann surfaces.

The fourth lecture will describe the Hitchin section and Hitchin components.
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