Sala Seminari (Dip. Matematica).
In this talk we will talk about the relationship between hyperbolic cone-structures and their holonomy representations. Any hyperbolic structure on a given closed compact and orientable surface S induces in a very natural way a representation of the fundamental group \pi_1(S) in the Lie group PSL(2,R), which encodes geometric data about the structure. The reverse problem to recover a hyperbolic cone-structure from a given representation is more arduous and longer. Even worse it is not always possible. In the first part of this talk we will consider this problem from a general viewpoint giving examples of representations that not arise as the holonomy of hyperbolic cone-structure. In the second part we focus our attention to a very special class of representations, namely purely hyperbolic representations. Sito web: http://people.dm.unipi.it/babygeometri/