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).