On the 12th December we will have a double bill. Along with the talk of Alix Deruelle, will also have Eleonora Di Nezza (IHES) who willtalk about *“Complex Monge-Ampère equations with prescribed singularities”*. Her talk will be at 2.45pm. The abstract is below.

Since the proof of the Calabi conjecture given by Yau, complex Monge-Ampère equations on compact Kähler manifolds have been intensively studied.

In this talk we consider complex Monge-Ampère equations with prescribed singularities. More precisely, we fix a potential and we show existence and uniqueness of solutions of complex Monge-Ampère equations which have the same singularity type of the model potential we chose. This result can be interpreted as a generalisation of Yau’s theorem (in this case the model potential is smooth).

As a corollary we obtain the existence of singular Kähler-Einstein metrics with prescribed singularities on general type and Calabi-Yau manifolds.

This is a joint work with Tamas Darvas and Chinh Lu.