Geometry Seminar
Long time existence of the Pluriclosed flow
Speaker: Luigi Vezzoni (Torino)Date: Friday, 24 April 2026 - 10:00Place: Aula Naranja, ICMAT
Abstract:
The pluriclosed flow was introduced by Streets and Tian in 2010 as a generalization of the Kähler–Ricci flow 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 the pluriclosed flow a promising tool for the classification of complex surfaces.
A fundamental open problem is to determine the maximal existence time of the pluriclosed flow. Streets and Tian conjectured that this is governed by a cohomological invariant known as the Aeppli–Chern class.
Important evidence for this conjecture comes from work of Streets and García-Fernández, who verified it on Bismut-flat manifolds and on minimal non-Kähler surfaces with nonnegative Kodaira dimension, as well as from work of Streets and Wang, who confirmed it on Oeljeklaus–Toma manifolds.
In this talk, we present new results on long-time existence in the presence of symmetries, focusing in particular on nilmanifolds and solvmanifolds, and more generally on Hermitian manifolds admitting a holomorphic submersion over a negatively curved Hermitian manifold.
This is joint work in progress with Elia Fusi and James Stanfield.
