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SUMMARY:(Leverhulme Lecture) Higher Teichmueller Theory: Geometric\, Arith
 metic\, and non-Archimedean Aspects. Part 2 —  On maximal representation
 s - Marc Burger (ETH Zurich)
DTSTART:20170317T134500Z
DTEND:20170317T150000Z
UID:TALK71327@talks.cam.ac.uk
CONTACT:Maurice Chiodo
DESCRIPTION:In this lecture we'll concentrate on maximal representations i
 nto Sp(2n\,R) and explain the role of bounded cohomology in their study: t
 his allows to extend the notion of maximality  to surfaces with boundary\,
  which classical cohomology would not provide\, and leads to Fenchel Niels
 en coordinates describing components of maximal representations. We will t
 hen show how very classical facts from hyperbolic geometry in dimension tw
 o\, like the collar lemma and the length inequalities obtained by splittin
 g self-intersecting geodesics generalise to this context\, while they fail
  for quasifuchsian representations into SL(2\,C).
LOCATION:CMS MR13
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