buondì, vi segnalo il seminario di geometria di domani, sempre alle 14 in aula seminari. a presto, Bruno ------ MARTEDI' 14 OTTOBRE 2014 SEMINARI DI GEOMETRIA 14:00-15:00, Sala Seminari (Dip. Matematica) Ergodicity of the mapping class group action on a component of the character variety. Juan Souto (CNRS - Université de Rennes) Abstract: Goldman proved that the variety X_g of conjugacy classes of representations of a surface group of genus g into PSL_2R has 4g-3 connected components X_g(2-2g), ... ,X_g(2g-2) indexed by the Euler number of the representations therein. The two extremal components X_g(2-2g) and X_g(2g-2) correspond to Teichmueller spaces on which the mapping class group acts discretely. On the other hand Goldman conjectured that the action on each one of the other components is ergodic. I will explain why this is indeed the case the component X_g(0) consisting of representations with Eulernumber 0 and for all g>=3. The basic technical result is a formula relating the euler number of a representation and the infimum of the energies of equivariant harmonic maps where the infimum is taken over all maps and all conformal structures on the surface of genus g.