Orateurs
- Henri Guenancia (Université de Bordeaux) : Some geometric applications of Kähler-Einstein metrics
In these lectures, I will explain how to derive some beautiful geometric applications from the existence and uniqueness of Kähler-Einstein metrics on compact Kähler manifolds obtained by Aubin and Yau in the late '70s. Applications will include the study of the fundamental group, the universal cover and the automorphism group of some complex projective or Kähler manifolds whose first Chern class has a sign.
- Eleonora Di Nezza (Université de Rome - Tor Vergata) : Existence and uniqueness of Kähler-Einstein metrics
These lectures will focus on the the existence, uniqueness, and regularity of special metrics on compact Kähler varieties, with particular emphasis on the Kähler–Einstein case in light of the celebrated theorems of Aubin-Yau and Chen-Donaldson-Sun. We will explain how this problem can be reformulated as the study of (possibly degenerate) complex Monge-Ampère equations, and we will introduce the main tools from pluripotential theory that are needed to analyze and solve such equations.
Emploi du temps et programme :
Mini-cours: Amphi L bâtiment 42 ESIR
Jeudi 1er octobre
- 14h - 15h : Eleonora Di Nezza 1, basic definitions, Kähler-Einstein metrics and examples
- 15h15 - 16h15 : Henri Guenancia 1, Uniformization theorems via Chern numbers
- 16h15 - 16h45 : Pause café (Hall de l'ESIR BAT 42)
- 16h45 - 17h45 : Eleonora Di Nezza 2, Monge-Ampère equations
Vendredi 2 octobre
- 9h - 10h : Henri Guenancia 2, Positive curvature
- 10h - 10h30 : Pause café (Salle de reunion de l'ESIR BAT 41 bis)
- 10h30 - 11h30 : Eleonora Di Nezza 3, A priori estimates
- 11h30 - 12h30 : Henri Guenancia 3, Zero curvature
- 12h30 - 14h : Cocktail déjeunatoire ( BAT 40 Salle 7 près de la bibliothèque)
- 14h - 15h : Henri Guenancia 4, Negative curvature
- 15h15 - 16h15 : Eleonora Di Nezza 4, Singular Kähler-Einstein metrics