Mathematical Sciences: NSF-CBMS-Regional Conference on Kaehler Geometry and Several Complex Variables; July, 1988

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One of the most beautiful results in the theory of complex analysis is the Riemann mapping theorem, which states that any simply connected open region in the plane is biholomorphic to the complex plane or to the open ball. In passing from analysis of one complex variable to several complex variables the situation becomes much more involved. In fact, a uniformization theorem like the Riemann mapping theorem is not possible. Riemann surfaces (surfaces with a complex structure) can be given a natural Kaehler structure, while higher dimensional complex manifolds need not be Kaehler. It is natural then, in some sense, to study uniformization theorems for Kaehler manifolds. The object of this conference will be to review work in this area, to discuss some recent results (as yet unpublished), and to lay the ground work for more activity in the future. Professor Y. T. Siu of Harvard University will be the principal lecturer and will give a series of ten talks.