Dynamics and moduli of geometries on surfaces

by Prof. William Goldman (University of Maryland)

Monday Dec 10, 2018, 2:30 PM → 3:45 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

We describe dynamical systems arising from the classification of locally homogeneous geometric structures on manifolds. Their classification mimics the classification of Riemann surfaces by the Riemann moduli space – the quotient of Teichmüller space by the properly discontinuous action of the mapping class group. However, this action is misleading: mapping class groups generally act chaotically on character varieties. For fundamental examples, these varieties appear as affine cubics, and we relate the projective geometry of cubic surfaces to dynamical properties of the action.