SCV India Online Seminars

Upcoming mini courses

Abstract: Levi-flat hypersurfaces appear as natural objects at the intersection of several different problems in several complex variables. They are pseudoconvex from both sides, they are invariant sets of holomorphic foliations, and they are simply the flat manifolds from the point of view of CR geometry. Singularities appear naturally and are a current topic of active research. We will assume basic theory of several complex variables, and we will cover all the background necessary, including CR geometry, the real-algebraic and analytic geometry, and basics of holomorphic foliations, to get to the current state of the art of Levi-flat hypersurfaces. The main technique we will consider in studying Levi-flat hypersurfaces is the Segre variety and the related techniques, which found many other uses in CR geometry.

Abstract: These lectures discuss peak sets for the unit disc in one complex variable and peak points for pseudoconvex domains in several variables. We highlight two open problems: characterizing peak sets for functions holomorphic on the unit disc and Lip-\alpha on the closure, and determining whether points of finite type are peak points for pseudoconvex domains with smooth boundary.