Interactions between people working in Index Theory and Complex Geometry are increasing. One of the reasons is that although researchers use different tools and techniques, their studies have profound connections and are understandable to people from both sides. Sharing experiences and techniques is an opportunity for them to accelerate collaboration works. Index Theory and Complex Geometry recently both have spectacular developments. In this program, we plan to dig out more materials on complex geometry side of global analysis led by recent development on geometric hypoelliptic Laplacians.
Another focus of our program will be the interaction of analytic localization technique in local index theory and complex geometry, for example, the study of Bergman Kernel.We expect that recent works in complex geometry, on pluripotential theory, the Hormander L2 method and the study of Bergman kernels would have many things to share with index theory.