Research Projects

The broad objective of this research proposal is to study the relationship between analytic discs and the geometry and function theory of CR singular manifolds. Analytic discs have served as a very useful tool in the study of geometry and function theory of CR manifolds (without singularities), especially in results concerning holomorphic extension of CR functions. A key ingredient to show holomorphic extension is the Baouendi-Trèves approximation theorem. Our aim is to explore the extent to which these results hold for CR singular manifolds, to tease out interconnections and dependencies, and hopefully discover new phenomena in the process. We are confident that our expertise in studying CR singular manifolds will help us make significant progress in this quest.