Abstract:
  Using meromorphic differentials with prescribed singular parts
and real
  periods on Riemann surfaces, we define a new foliation of M_g and
give a
  quick proof of the Diaz' bound on the dimension of complete
  subvarieties of M_g. We will also discuss potential further
application
  of this foliation (motivated by the Whitham perturbation theory
of
  integrable systems) to the study of cohomology and subvarieties
of M_g.
  Joint work with Igor Krichever.