Dear all,
a PhD course on "Complex Monge-Ampère equations on compact Kähler manifolds" will be taught by Chinh H. Lu in Firenze. The course will take place between February and May 2016, at Dipartimento di Matematica e Informatica "Ulisse Dini" of Università di Firenze. You find here below the abstract.
A first preliminary meeting is scheduled for: monday February 01, 2016, at 13:00. The calendar of the course will be scheduled in that occasion.
Further and updated informations will be available at the webpage of the event on GeCoGeDi https://gecogedi.dimai.unifi.it/event/294/.
Please, feel free to contact us if you are interested in attending the course. And to forward this message to whoever might be interested in it.
The course is supported by the project SIR2014 "Analytic aspects in complex and hypercomplex geometry" https://sites.google.com/site/danieleangella/projects/anhyc and it is part of the PhD program in Mathematics of Università di Firenze http://www.dimai.unifi.it/vp-26-dottorati.html.
Best regards, Daniele Angella, Simone Calamai
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Title: "Complex Monge-Ampère equations on compact Kähler manifolds"
Number of hours: 30h / 6 CFU (20h by Chinh, 10h of preparation in complex geometry by Daniele)
Period: starting from the middle of February until middle of May
Place: Firenze
Program:
The aim of the course is to survey recent important results concerning the complex Monge-Ampère equation on compact Kähler manifolds. We first present the proof of the Calabi conjecture by reducing it to a complex Monge-Ampère equation and establishing a priori estimates. We then go on to develop a (global) pluripotential theory on compact Kähler manifold, focusing on the theory of (generalized) capacities and its application in proving singular uniform estimate. We also introduce a variational method to solve degenerate complex Monge-Ampère equation and study the finite energy spaces which will be recognized as the completion of the space of Kähler metircs equipped with the Mabuchi distance. The last lecture will be a more advanced talk (materials from previous lectures will be useful) on the weak Calabi flow, its large time behavior as well as some conjectures in the field.
A preliminary part of the course will discuss basic results on complex and Kähler geometry.
Teacher: Chinh H. Lu Centro di Ricerca Matematica "Ennio de Giorgi", Pisa chinh.lu@sns.it https://sites.google.com/a/sns.it/chinh-h-lu/home
Collaborator: Daniele Angella DiMai "Dini", Università di Firenze daniele.angella@gmail.com, daniele.angella@unifi.it https://sites.google.com/site/danieleangella/