Special Colloquium
Speaker: Ved Datar (Indian Institute of Science)
Host: Anusha Mangala Krishnan
Title: The Kobayashi-Hitchin principle in complex geometry
Time, day and date: 11:30:00 AM - 12:30:00 PM, Thursday, August 28
Venue: Ramanujan Hall
Abstract: A very general principle lies at the heart of complex differential geometry - existence of canonical differential geometric objects on projective manifolds (metrics, connections, solutions to non-linear PDEs etc) must be equivalent to a purely algebro-geometric notion called “stability”. The first example of such a correspondence was the famous Narasimhan-Seshadri theorem. Since then, this general principle has become ubiquitous in all of complex differential geometry and is now the single most important way to arrive at new conjectures. I will illustrate this principle by way of two examples that have seen impressive progress over the last two decades and yet continue to remain active areas of research - existence of K\”ahler-Einstein metrics on Fano manifolds and existence of
solutions to some fully non-linear PDEs such as the $J$-equation.