Speakers: Dr Xiao Jia (PKU)

Place: 全斋 29， Math Center.

Time: May 6 (Tuesday), 10:10am-12:00pm

Abstract: In this talk, we will discuss a paper by Bo Berndtsson:《A Brunn-Minkowski Inequality for Fano Manifolds and Some Uniqueness Theorems in Kahler Geometry》. In the paper, he proved that the volume of a Fano manifold X with respect to a metric on the anti-canonical bundle is logarithm concave along geodesics in the space of positively curved metrics on the anti-canonical bundle. Moreover, the concavity is strict unless the geodesic comes from the flow of a holomorphic vector field of X. We will go over his proof.