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 prévisionnel 

Mini-cours: Amphi L bâtiment 42

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

    Pause café

  • 16h45 - 17h45 : Eleonora Di Nezza 2, Monge-Ampère equations

Vendredi 2 octobre

  • 9h - 10h : Henri Guenancia  2, Positive curvature

Pause café

  • 10h30 - 11h30 : Eleonora Di Nezza 3, A priori estimates 
  • 11h30 - 12h30 : Henri Guenancia  3, Zero curvature 

Pause déjeuner

  • 14h - 15h : Henri Guenancia 4, Negative curvature
  • 15h15 - 16h15 : Eleonora Di Nezza 4, Singular Kähler-Einstein metrics