Abstract: Let X be a Riemann surface, and þ an n-dimensional irreducible representation of the fundamental group of X. If n=1, þ gives rise to a 1-dimensional representation of \pi_1(Pix(X)). If n>1, it turns out that to þ one can associate a certain topological object "living" on the moduli space of rank n holomorphic vector bundles on X. In the talk we will explain this constrution and its connection with the classical Langlands' program.