2 may 2019 -- 14:30
Aula Tricerri, DiMaI, Firenze
In the 1950s Calabi asked the question of whether a compact complex manifold admits a preferred Kähler metric, distinguished by natural conditions on the volume or the Ricci tensor. Following recent important advances in Kähler geometry, such as the solution of the Kähler-Einstein problem by Donaldson, Chen and Sun, there is a renewed interest in extending Calabi's Programme to the case of compact complex manifolds which do not admit a Kähler metric. In this talk I will discuss a concrete proposal for a theory of canonical metrics in complex non-Kähler geometry, inspired by string theory and based on holomorphic Courant algebroids. If time allows, I will also comment on a potential extensión of mirror symmetry for these new geometries.