The pluriclosed flow on complex surfaces

Giuseppe Barbaro (Aarhus University)

Tuesday 4th February 15:00-16:00 Maths 311B

Abstract

We recall fundamental aspects of the pluriclosed flow equation introduced by Streets and Tian as a generalization of the Ricci flow in the Hermitian non-K\”ahler context. Building on this, a precise conjectural description of the long time behavior of the flow on complex surfaces is formulate, which has implications for the classification of  complex surfaces through the GSS conjecture. We describe some of the existence and convergence results, focusing on the case of Bismut flat manifolds and Vaisman surfaces.

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