Higher rank Teichmüller spaces and Higgs bundles (Oscar GARCIA-PRADA, ICMAT Madrid)

15.10.2024 15:00 – 16:00

It is well-known that the Teichmüller space of a compact 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 rank Teichmüller spaces are generalizations of this, which exist in the moduli space of representations of the fundamental group into certain real simple non-compact Lie groups of higher rank. As for the usual Teichmüller space, these spaces consist entirely of discrete and faithful representations. In this series of lectures, I will give a full classification of the groups for which higher rank Teichmüller spaces can exist, as well as a complex algebraic-geometric parametrization of these spaces in terms of Higgs bundles. This involves, in particular, the non-abelian Hodge correspondence, and the more recent Cayley correspondence developed in collaboration with Steve Bradlow, Brian Collier, Peter Gothen and André Oliveira (to appear in Annals of Mathematics, 2024, arXiv:2101.09377).

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Mini-cours

entrée libre