School Seminars and Colloquia

Globally Existing Kahler-Ricci Flow

Algebra/Geometry/Topology Seminar

by Zhang Zhou

Institution: University of Sydney
Date: Fri 31st May 2013
Time: 3:30 PM
Location: 213 Richard Berry

Abstract: Kahler-Ricci flow has an equivalent form as the parabolic
version of complex Monge-Ampere equation. The limiting equation at
time infinity is nothing but the Kahler-Einstein Equation. We focus on
the version which is most robust when the flow has global existence,
i.e. existing for all time. In the non-degenerate case, the flow
metric smoothly converges to the Kahler-Einstein metric without
assumption on the initial Kahler class. In the degenerate case,
singularities has to be developed. In principle, the analysis of them
improves the understanding of the (singular) Kahler-Einstein metric as
the limit. We survey some recent results and discuss further problems.