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京东 11.11 红包
Jeffrey Streets:Pluriclosed flow and the Hull Strominger system
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https://www.youtube.com/watch?v=4AxRhxi0eZ8 Frontiers of Geometric Analysis In honor of Gang Tian's 65th birthday 3-7 June 2024 Santa Cruz, California Jeffrey STREETS, University of California, Irvine, USA Abstract: The Hull-Strominger system arose in superstring theory, and is a subject of intense mathematical interest due to its connection to uniformization problems in complex geometry. I will discuss a mild reformulation of this system, and show that the tools of pluriclosed flow/generalized Ricci flow can be used to construct solutions to this system. This point of view leads to a proof of smooth regularity of uniformly elliptic solutions of the Hull-Strominger system. Joint work with M. Garcia-Fernandez and R. Gonzalez-Molina. Mario Garcia-Fernandez, Raul Gonzalez Molina, Jeffrey Streets——“Pluriclosed flow and the Hull-Strominger system”:https://doi.org/10.48550/arXiv.2408.11674 We define a natural extension of pluriclosed flow aiming at constructing solutions of the Hull-Strominger system. We give several geometric formulations of this flow, which yield a series of a priori estimates for the flow and also for the Hull-Strominger system. The evolution equations are derived using the theory of string algebroids, a class of Courant algebroids which occur naturally in higher gauge theory. Using this, we interpret the flow as generalized Ricci flow and also as a higher/coupled version of Hermitian-Yang-Mills flow, proving furthermore that it is compatible with symmetry reduction. Regarding our main analytical results, we prove a priori C∞ estimates for uniformly parabolic solutions. This in particular settles the question of smooth regularity of uniformly elliptic solutions of the Hull-Strominger system, generalizing Yau's C3 estimate for the complex Monge-Ampère equation. We prove global existence and convergence results for the flow on special backgrounds, and discuss a conjectural relationship of the flow to the geometrization of Reid's fantasy.
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