2022-02-21 Seminar Report

Dr. Genki Hosono gave us a stimulating talk on pluripotential and $L^2$ methods in complex geometry. The talk was carefully designed not only for non-mathematicians but also for experts around the topic. He began his talk with the definition and basic properties of subharmonic function and its multivariable version in complex geometry: plurisubharmonic function. He then introduced Bergman kernel and explained a variational approach to Ohsawa-Takegoshi $L^2$ extension theorem, which is an extension theorem of holomorphic function with a bound on $L^2$ norm weighted by a plurisubharmonic function. Finally he explained Deng-Wang-Zhang-Zhou’s result on a `reverse direction’ of Ohsawa-Takegoshi theorem and his result with Inayama on a variant result. His explanations were very clear and quite valuable for us.

Reported by Eiji Inoue

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