Pluriclosed flows in the presence of symmetry

Pluriclosed flows were introduced by Streets and Tian in 2009 as a generalisation of Kähler–Ricci flows to pluriclosed metrics, a class of Hermitian metrics on complex manifolds that strictly contains the class of Kähler metrics. Pluriclosed metrics arise naturally in physics and exist on every complex surface, making pluriclosed flows a promising tool for the classification of complex surfaces. A fundamental open problem is to determine the maximal existence time of a pluriclosed flow. It is conjectured that this is governed by a cohomological invariant known as the Aeppli–Chern class. In this talk, we present results confirming this conjecture in several symmetric settings. In particular, we prove that (not-necessarily invariant) pluriclosed flows are immortal on nilmanifolds.

This is joint work with Elia Fusi, and Luigi Vezzoni (Torino).