Room P3.10, Mathematics Building

Éveline Legendre, Université Paul Sabatier, Toulouse
Commonness of Kähler-Einstein metrics in toric geometry

I will explain why each integral convex compact polytope is the moment polytope of a Kähler-Einstein orbifold (unique up to a dilatation). More generally, I will explain how to prove that each convex compact polytope admits a unique ray of symplectic potentials solving the toric Kähler-Einstein equation. Then, I'll bring out some geometric applications.