Abstract: Kallin's Lemma is a technical tool useful for proving the polynomial convexity of certain unions of polynomially convex compacts (such as the union of 3-balls). We show that this result extends to holomorphically convex compacts in a Stein manifold. We will define Kallin's Lemma, introduce the necessary background from the theories of uniform algebras and Stein manifolds, and prove the generalization.

This is a PhD Comprehensive Examination.

Speaker's web page: http://www.math.uwo.ca/index.php/profile/view/208/