Skeleta of Stein varieties and Homological Mirror Symmetry in the large complex limit

In this talk I will report on joint work with Ruddat, Treumann, and Zaslow. We construct an explicit geometric model for the skeleton of a Stein hypersurface in toric ambient space. This has applications to the study of the Fukaya category of Stein varieties (sheaf theoretic methods, advocated by Kontsevich and others, play an important role here), and Homological Mirror Symmetry in the large complex limit.