Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Anton Mellit
Affiliation:

University of Vienna
Date:

Tue, 2018-02-06 14:00 - 15:00 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.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/5312