Schiffmann obtained a formula for the (weighted) number of vector bundles with nilpotent endomorphism over a curve over a finite field.

This talk will be about counting parabolic bundles with nilpotent endomorphism. The result we obtain gives an interesting new interpretation of Macdonald polynomials. Our formula turns out to be similar to the conjecture of Hausel, Letellier and Rodriguez-Villegas, which gives the mixed Hodge polynomials of character varieties. This allows us to obtain a new confirmation of their conjecture : we prove its implication for the Poincare polynomials of character varieties.