28 nov 2017 -- 12:00
Aula Tricerri, DiMaI, Firenze
Abstract.
An important question in complex geometry is the existence of "canonical" Kähler metrics on polarised smooth projective varieties. An extremal Kähler metric, as defined by E. Calabi, is widely considered canonical, and it can be regarded as a generalisation of constant scalar curvature Kähler or Kähler-Einstein metrics. Establishing the existence of extremal metrics amounts to solving a fully nonlinear PDE, but what is known as Yau-Tian-Donaldson conjecture states that it has a deep connection to stability notions in algebraic geometry. After explaining the background of this conjecture in the first part of the talk, we introduce some results to see how the Bergman kernel plays an important role in this theory.