Prof. V. Tosatti: The Chern-Ricci Flow

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Venue:DM 409A

Abstract: I will discuss the evolution of a Hermitian metric on a compact complex manifold by its Chern-Ricci curvature. This is an evolution equation which coincides with the Ricci flow if the initial metric is Kahler, and was first studied by M.Gill. I will describe the maximal existence time for the flow in terms of the initial data, and then discuss the behavior of the flow on (mostly non-Kahler) complex surfaces as one approaches the maximal existence time. This is joint work with Ben Weinkove and partly with Xiaokui Yang.