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Anosov representations and proper actions

Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015

April 14, 2015 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Fanny Kassel (Institut des Hautes Études Scientifiques (IHES))
Location: MSRI: Simons Auditorium
  • quotient manifolds

  • discrete subgroups

  • orthogonal and unitary groups of non-definite signature

  • Lorentz group

  • Cartan decomposition

  • proper actions

  • parabolic subgroup

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



Anosov representations of word hyperbolic groups into reductive Lie groups provide a generalization of convex cocompact representations to higher real rank. I will explain how these representations can be used to construct properly discontinuous actions on homogeneous spaces. For a rank-one simple group G, this construction covers all proper actions on G, by left and right multiplication, of quasi-isometrically embedded discrete subgroups of G×G; in particular, such actions remain proper after small deformations, and we can describe them explicitly. This is joint work with F. Guéritaud, O. Guichard, and A. Wienhard. 

23390?type=thumb Kassel.Notes 717 KB application/pdf Download
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H.264 Video 14218.mp4 366 MB video/mp4 rtsp://videos.msri.org/data/000/023/279/original/14218.mp4 Download
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