We use a pair of meromorphic differentials on a Riemann surface
with all periods real to construct real foliations of
*M _{g}* with complex leaves. This structure allows us to
bound the possible number of common zeroes of these two
differentials. One application of this is a new proof of
vanishing of some tautological classes in cohomology. Another
application is a new bound for the maximal number of cusps of
plane curves. Joint work in progress with Igor Krichever, but
Krichever's talk is not a prerequisite.