Colloquium
3:00 p.m., Friday (January 12, 2007)
MATX 1110
Jian Song
John Hopkins University
Canonical Kahler metrics and the KahlerRicci flow
The existence of KahlerEinstein metrics on a compact Kahler manifold
of definite or vanishing first Chern class has been the subject of intense
study over the last few decades, following Yau's solution to Calabi's
conjecture. The KahlerRicci flow is the most canonical way to construct
KahlerEinstein metrics. We define and prove the existence of a family
of new canonical metrics on projective manifolds with semiample canonical
bundle, where the first Chern class is semidefinite. Such a generalized
KahlerEinstein metric can be constructed as the singular collapsing
limit by the KahlerRicci flow on minimal surfaces of Kodaira dimension
one. Some recent results of KahlerEinstein metrics on Kahler
manifolds of positive first Chern class will also be discussed.
Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge).
