Geometric Analysis and Topology Seminar

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L^2 Extension of Holomorphic Functions from Algebraic Hypersurfaces

Speaker: Dror Varolin, Stony Brook University

Location: Warren Weaver Hall 1013

Date: Friday, March 6, 2009, 1 p.m.

Synopsis:

We discuss the problem of extension of holomorphic functions from a possibly singular analytic hypersurface. We show that, in a very precise sense, if the hypersurface (i) is not too dense and (ii) has rather mild singularities, then such extension is possible. In the case where the hypersurface is algebraic, this density condition is automatically satisfied, and we show that the sufficient condition on the singularities of the hypersurface is also necessary. If time permits we will indicate why we have not yet been able to establish the necessity of our conditions in the case of analytic hypersurfaces.