For this semester will hold this meeting online. All researchers and students with interest in this area are welcome to attend, we look forward to seeing many of you there. Zoom links will be posted here.
Abstract: In a lot of geometric situations we need to work with families of varieties. In this talk we focus on families of singular Kähler-Einstein metric. In particular we study the case of a family of Kähler varieties and we develop the first steps of pluripotential theory in family, which will allow us to have a control on the C^0 estimate when the complex structure varies. This type of result will be applied in different geometric contexts. This is a joint work with V. Guedj and H. Guenancia.
The laws of nature at its most fundamental level have long been a source of inspiration for geometry and partial differential equations. With unified string theories and particularly supersymmetry, a particularly important new requirement has emerged, which is that of special holonomy. The earliest manifestation was identified by Candelas, Horowitz, Strominger, and Witten in 1985 as the Calabi-Yau condition, but more general spaces have emerged since, which can be interpreted as generalizations of Calabi-Yau spaces to both non-Kaehler complex geometry and symplectic geometry. The corresponding equations are interesting in their own right from the point of view of the theory of non-linear partial differential equations. We shall survey some of these developments, with emphasis on the analytic open problems.