Macdonald polynomials and counting parabolic bundles

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.