Séminaires : Groupes, Représentations et Géométrie

Equipe(s) : gr,
Responsables :Adrien Brochier, Olivier Brunat, Jean-Yves Charbonnel, Olivier Dudas, Daniel Juteau, Emmanuel Letellier, Michela Varagnolo, Eric Vasserot
Email des responsables : adrien.brochier@imj-prg.fr ; olivier.brunat@imj-prg.fr; jean-yves.charbonnel@imj-prg.fr; olivier.dudas@imj-prg.fr; emmanuel.letellier@imj-prg.fr; daniel.juteau@imj-prg.fr; varagnol@math.u-cergy.fr; eric.vasserot@imj-prg.fr
Salle : 1016
Adresse :Sophie Germain

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Orateur(s) Oscar Garcia-Prada - ICMAT, Madrid,
Titre iggs bundles and higher Teichmüller spaces
Horaire10:30 à 12:15
RésumeThe Teichmüller space of a compact real surface, parameterising complex structures on the surface, can be identified with a connected component of the moduli space of representations of the fundamental group of the surface in PSL(2,R). Higher Teichmüller spaces are generalizations of this, where PSL(2,R) is replaced by certain simple non-compact real Lie groups of higher rank. As for the usual Teichmüller space, these spaces consist entirely of discrete and faithful representations. Several cases have been identified over the years. First, the Hitchin components for split groups, then the maximal Toledo invariant components for Hermitian groups, and more recently certain components for SO(p,q). In the first 45 minutes, after giving some background on Higgs bundle theory and the non-abelian Hodge correspondence, I will review the cases mentioned above. In the second part of the talk, I will present a general construction in terms of Higgs bundles of the higher Teichmüller spaces. Key ingredients in this construction are the notion of magical sl(2)-triple, that we introduce, and the Cayley correspondence (based on joint work with Bradlow, Collier, Gothen and Oliveira).
AdresseSophie Germain