Cursos
Canonical metrics in complex geometry - Part 1: Kahler geometry
Ponente: Federico Giusti (ICMAT)Fecha: lunes 24 de febrero de 2025 - 10:30-12:30Lugar: Aula Gris 2, ICMAT
Resumen:
The problem of canonical metrics has been fueling the research in Kahler geometry for many decades, leading to several groundbreaking results along with also some still-standing open problems. In recent years, also the non-Kahler world has been very interested in canonical metric, facing the primary problem of identifying what canonical metrics should look like in this context, mainly due to the les evident algebraic nature of complex non-Kahler geometry.
The following course will be divided into two main parts. The first one will be focused on the Kahler setting, where we will mainly look into canonical Kahler metrics - which are recognized to correspond to the so-called "Extremal metrics" - and the central results which justify the "canonical" label. The second part will instead drift away from the Kahler world, and we will be discussing the various possible paths - suggested by the Kahler setup - to search for a notion of canonical metric in the non-Kahler setting, by seeing some recent interesting results and several open problems being central in the field. A class of manifolds we will place special attention in is the one of balanced manifolds, i.e. manifolds admitting a co-closed hermitian metric, which are at the center of several conjectures and are one of the most understood families in the non-Kahler setting.
Schedule:
Part 1: Kahler geometry
24th Feb: 10:30-12:30, Gris 2
28th Feb: 10:30-12:30, Gris 1
3rd March: 10:30-12:30, Gris 2
7th March: 10:30-12:30, Gris 2
Part 2 - Non-Kahler geometry
24th March: 10:30-12:30, Gris 2
4th April: 10:30-12:30, Gris 1
7th April: 10:30-12:30, Gris 3
11th April: 10:30-12:30, Gris 1
