Seminar:Calabi-Yau metrics on noncompact manifolds

Time:

Venue/Location: Phòng C101, VIASM

Báo cáo viên: Nghiêm Trần Trung (Đại học Claude Bernard Lyon 1)

Tóm tắt: The seminal works of Yau and Calabi show that there is always a unique Calabi--Yau metric in a Kahler class of a compact manifold with zero first Chern class. On noncompact manifolds, however, the classification remains largely open. In the case where the manifold sits inside a Fano compactification with a Fano Kahler--Einstein smooth divisor, Tian and Yau established the existence of Calabi--Yau metrics, which turn out to be asymptotically conical (AC). A recent article of Conlon and Hein classified all possible Calabi--Yau manifolds asymptotic to a given Calabi--Yau cone with smooth link. A natural reciprocal question is to classify all AC Calabi--Yau metrics on a given manifold. After a survey on the state of the art, I'll mention the classification of AC Calabi--Yau metrics on complex symmetric spaces. This is mostly based on my thesis.