Kähler-Ricci solitons and toric geometry

Nom de l'orateur
Charles Cifarelli
Etablissement de l'orateur
LMJL
Date et heure de l'exposé
Lieu de l'exposé
Salle de séminaire

Kähler-Ricci solitons are a natural generalization of the concept of a Kähler-Einstein metric which arise in the study of the Kähler-Ricci flow. In particular, shrinking gradient Kähler-Ricci solitons on non-compact manifolds model the singularity development of the Kähler-Ricci flow. In this talk, I will present some of my thesis work on the uniqueness of shrinking gradient Kähler-Ricci solitons on non-compact toric manifolds. In particular, the standard product of the Fubini-Study metric on $\mathbb{CP}^1$ (the round metric on $S^2$) and the Euclidean metric on $\mathbb{C}$ is the only shrinking gradient Kähler-Ricci soliton on $\mathbb{CP}^1 \times \mathbb{C}$ with bounded scalar curvature.