Speaker: Terry Napier, Lehigh University

Title: The Bochner--Hartogs dichotomy

Abstract: In 1906, Friedrich Hartogs discovered that a complex analytic function defined near the boundary of a ball in complex Euclidean space of dimension n>1 must extend complex analytically to the entire ball. In particular, in dimension n>1, all isolated singularities are removable. This was perhaps the first hint that convexity (of some sort) should play an important role in the study of several complex variables. In this talk, we will consider briefly how this idea developed over the next 100 years, and consider analogues of Hartogs' extension theorem in the general setting of Kaehler manifolds.

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