Colloque des sciences mathématiques du Québec

14 septembre 2007 de 16 h 00 à 18 h 00 (heure de Montréal/HNE) Sur place

Geometry and Dynamics of Surface Group Representations

Colloque par William Goldman (University of Maryland)

The space of representations of the fundamental group of a surface in a Lie group is a rich geometric object. Examples include symplectic vector spaces, Jacobi varieties and Teichmueller spaces. The topological symmetries of the surface acts on this space preserving a natural Poisson geometry. This action of the mapping class group closely relates to Hamiltonian flows on these moduli spaces. When the Lie group is compact, the action is chaotic. For uniformization representations corresponding to geometric structures, the action is properly discontinuous. In general the dynamics falls between these two extremes.


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