Dolbeault cohomology on symplectic four-manifolds
-- Stanislav Jabuka, April 4, 2003

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We define an extension of the notion of Dolbeault cohomology
  to the case of symplectic four-manifolds. The definition
  depends on the choice of an almost-complex structure J and
  the first part of the talk investigates how the cohomology
  changes as one varies J.  The second part of the seminar
  considers several examples and provides explicit calculations
  of the cohomology groups.  The talk concludes with an
  application of the cohomology groups to the question of
  comparing the symplectic to the Kahler cone on a Kahler
  manifold.