Dr. Zhou Zhang 短期课程


题目:Pluripotential Theory with Applications in Differential Geometry

报告人:Dr. Zhou Zhang, the University of Sydney

时间:2014.9.1-9.30  每周二周四  18:30--21:00  共四周


摘要: complex Monge-Ampere equation and related topics have been at the central stage of complex differential geometry for more than three decades. In the past ten years or so, the new input from pluripotential theory has brought new life to this field of research.
We start with an overall description of the original L estimate by S lawomir Ko lodziej, as one of the most essential new ingredients. Then for the major part of this course, we provide the introduction of pluripotential theory and the detail of that argument, with an eye on possible alternatives and the crucial generalization to various degenerate settings. If time allows, towards the end of the series, we would discuss other developments in the theory itself (for example, regarding unbounded plurisubharmonic function) and the applications to differential geometry (for example, the new proof of the convexity of K-energy by Berman-Berndtsson).
We hope to keep it an entry level graduate course. Some knowledge about subharmonic function and complex manifold would certainly be helpful.


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