5 sep 2018 -- 15:00
Aula 4, Dipartimento di Matematica "G. Peano" dell'Università di Torino
Abstract.
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 advances in Kähler geometry, 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. The equations that define our notion of "best metric" are motivated by generalized geometry, and correspond to a mild generalization of the Hull-Strominger system. Joint work with R. Rubio, C. Shahbazi and C. Tipler, arXiv:1803.01873, arXiv:1807.10329