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SUMMARY:Slices of Representations of Surface Groups in $G_2$ and Associate
 d Geometric Structures
DTSTART:20260112T150000Z
DTEND:20260112T161500Z
DTSTAMP:20260313T173400Z
UID:indico-event-15739@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Colin Davalo (Università di Torino)\n\nIn this talk
  we will consider two families of representations from the fundamental gro
 up of a closed surface of genus at least 2 into the exceptional Lie group 
 G2\, and more precisely into its real split form G2'. Representations in t
 hese families correspond to Higgs bundles of a very special form introduce
 d by Collier and Toulisse. They come with associated equivariant objects: 
 they admit an alternating almost-complex map into the pseudosphere S2\,4\,
  which can be reinterpreted as a parallel distribution of planes along a m
 inimal surface in the symmetric space.\nFrom the Higgs bundle description 
 of these families\, however\, it is far from clear whether these represent
 ations have good geometric properties. In joint work with Parker Evans\, w
 e use the equivariant objects to construct explicitly a geometric structur
 e associated to some of these representations.\nAfter an introduction to t
 he geometry of G2' and to these two families of representations\, I will 
 present our results explaining how to construct for every representation 
 ρ in the first family a geometric structure modelled on a flag manifold o
 f G2\, the Einstein universe Ein2\,3\, whose holonomy is ρ. This is a str
 ucture on a fiber bundle over the considered surface with fiber diffeomorp
 hic to Ein2\,1.\n \n\nhttps://indico.math.cnrs.fr/event/15739/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/15739/
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