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Recent progress in anomaly flow

Banff International Research Station for Mathematical Innovation and Discovery

The Hull-Strominger system describes the geometry of compactifications of heterotic superstrings with flux, which can be viewed as a generalization of Ricciflat Kahler metrics on non-Kahler Calabi-Yau manifolds. To overcome the difficulty of lacking ddbar-lemma, Phong-Picard-Zhang initiated the program of Anomaly flow to understand the Hull-Strominger system. It has been proved in many cases that the Anomaly flow serves as an effective way to investigate the Hull-Strominger system and in general canonical metrics on complex manifolds, such as giving new proofs of the Calabi-Yau theorem and the existence of Fu-Yau solution. In this talk, we present some new progress on the Anomaly flow, including the behavior of Anomaly flow on generalized Calabi-Gray manifolds and a unification of the Anomaly flow with vanishing slope parameter and the Kahler-Ricci flow, which further allows us to generalize the notion of the Anomaly flow to arbitrary complex manifolds. This talk is based on joint work with Z.-J. Huang, D.H. Phong and S. Picard.

Mathematics; Differential geometry; Algebraic geometry

video/mp4

Author affiliation: Columbia University

2020-04-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/74176

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/