Pairs of real normalized differentials, cohomology of <i>M<sub>g</sub></i>, and
cusps of plane curves -- Samuel Grushevsky, February 17, 2012

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We use a pair of meromorphic differentials on a Riemann surface
with all periods real to construct real foliations of
<i>M<sub>g</sub></i> 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.