Frederick Tsz-Ho Fong

Kähler-Ricci flow on manifolds with semiample canonical bundles

In this talk, the speaker will give a survey over both past and recent progress on the Kähler-Ricci flow on compact Kähler manifolds with semiample canonical line bundles. Under this setup, the underlying manifold admits a fibration structure with generic Calabi-Yau fibers, and the Kähler-Ricci flow admits a long-time solution which would converge to a generalized Kähler-Einstein metric. The speaker will give discuss the regularity of such a convergence, and its relation to the boundedness of various curvatures along the flow. Part of the results were joint works with Yashan Zhang, and with M.C. Lee.