Zero cycles on moduli spaces of curves

Tautological zero cycles form a one-dimensional subspace of the set of
all algebraic zero-cycles on the moduli space of stable curves. The full
group of zero cycles can in general be infinite-dimensional, so not all
points of the moduli space will represent a tautological class. In the talk,
I will present geometric conditions ensuring that a pointed curve does
define a tautological point. On the other hand, given any point Q in the
moduli space we can find other points P_1, ..., P_m such that Q+P_1+ ... +
P_m is tautological. The necessary number m is uniformly bounded in terms of
g,n, but the question of its minimal value is open. This is joint work with
R. Pandharipande.