3:00 p.m., Friday (January 12, 2007)
John Hopkins University
Canonical Kahler metrics and the Kahler-Ricci flow
The existence of Kahler-Einstein 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 Kahler-Ricci flow is the most canonical way to construct
Kahler-Einstein metrics. We define and prove the existence of a family
of new canonical metrics on projective manifolds with semi-ample canonical
bundle, where the first Chern class is semi-definite. Such a generalized
Kahler-Einstein metric can be constructed as the singular collapsing
limit by the Kahler-Ricci flow on minimal surfaces of Kodaira dimension
one. Some recent results of Kahler-Einstein 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).