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SUMMARY:Maximal representations of complex hyperbolic lattices in infinite
  dimension.
DTSTART:20190321T133000
DTEND:20190321T143000
DTSTAMP:20260407T064218Z
UID:1ac0fa86ee08c13e91df0add6d10e62a317c99a4c261fc4c32bf06ee
CATEGORIES:Conferences - Seminars
DESCRIPTION:Bruno Duchesne (Nancy)\nUnlike lattices in higher rank\, latti
 ces of simple Lie groups in rank 1 are not rigid. This gives rise to the T
 eichmüller spaces for example.\nFor representations of lattices of the is
 ometry group of the complex hyperbolic lattices in Hermitian Lie groups\, 
 the Kähler form yields a numerical invariant\, the Toledo number. When th
 is number is maximal\, these representations are rigid when the dimension 
 is at least 2.\nWe will focus on infinite dimensional representations of c
 omplex hyperbolic lattices that are not unitary but preserve a Hermitian f
 orm of finite index. This gives actions by isometries on infinite dimensio
 nal Hermitian symmetric spaces and one can define a Toledo number as well.
 \nWe will see that for surface groups\, one can create maximal representat
 ions that do not preserve any finite dimensional subspace. Conversely\, fo
 r complex hyperbolic lattices in dimension at least 2\, these maximal repr
 esentations factor through a finite dimensional Lie subgroup.
LOCATION:GR A3 30 https://plan.epfl.ch/?room==GR%20A3%2030
STATUS:CONFIRMED
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