Kähler geometry and connections on vector bundles have played an important role in mathematics as well as physics. The proposed programme is aimed at exposing young researchers to this vibrant field of research, and to some of the spectacular developments made in the field, over the past decade.
The programme consists of two components; - a school in the first week, followed by a workshop in the second week. The talks shall be largely centred around recent developments in Kähler geometry, particularly focussing, on the analysis of Monge-Ampère type PDEs, that arise out of geometric questions such as existence and degenerations of Kähler-Einstein metrics, and their relationship with algebraic geometry. The school will consist of mini courses on the following topics, and will be accessible to PhD students and highly motivated Master’s students with some experience in complex and Riemannian geometry.
1. The Calabi Conjecture and its applications.
2. Pluripotential theory and its role in Kähler geometry.
3. Gromov-Hausdorff convergence and L2 methods in Kähler geometry.
The topics covered in the first week of the program will help participants to prepare for the lectures during the following week. The workshop conducted during the second week of the program will consist of research talks by leading experts in complex geometry on topics of current interest.
Applications are invited from PhD students, post- doctoral fellows and faculty members, working in Kähler geometry and related areas of differential geometry and geometric analysis. Masters students showcasing mathematical creativity will also be considered.