Volume and proportionality of the moduli of Shtukas

The volume of a locally symmetric space is essentially a product of special values of zeta functions. More generally, Hirzebruch's proportionality theorem (extended by Mumford) tells us how to integrate any Chern class polynomial on a locally symmetric space.
We give an analog and extension of these results in the function field case where new phenomena show up. Locally symmetric spaces will be replaced by the moduli space of Drinfeld Shtukas with multiple legs, and special values of zeta functions will be replaced by a linear combination of their derivatives of various order. This is joint work with Tony Feng and Wei Zhang.