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Title:
Generalized Kahler Calabi-Yau problem
Speaker:
Abstract:
We formulate an extension of the Calabi conjecture to the setting of generalized Kahler geometry. We will discuss a new transgression formula for the Bismut Ricci curvature in this setting and use that to show solutions of the generalized Calabi-Yau equation on compact manifolds are classically Kähler, Calabi-Yau, and furthermore unique in their generalized Kähler class. We will also discuss how the generalized Kähler-Ricci flow is naturally adapted to the existence of solutions to the generalized Calabi-Yau equation. In particular, we will show the global existence and convergence of GKRF assuming that there is a generalized Calabi-Yau structure. The talk is based on joint work with Vesti Apostolov, Jeffrey Streets and Yury Ustinovskiy.
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