中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

多复变与复几何学术活动

Some Topics in Several Complex Variables

报告人宁家福 (副教授)(中南大学)

 Berndtsson’s proof of the Bourgain-Milman theorem

  127(星期三), 18:30-21:30

  点:腾讯会议:433-884-372

摘 要I will give a report on the Bourgain-Milman theorem. Berndtsson used complex methods to give a proof. I’ll talk about his papers. However, the best constant for the Bourgain-Milman theorem is still unsolved.

Reference:

·Berndtsson, Complex integrals and Kuperberg's proof of the Bourgain-Milman theorem, Advances in Mathematics, 388, 2021.

·Berndtsson, Bergman kernels for Paley-Wiener spaces and Nazarov's proof of the Bourgain-Milman theorem, Pure and Applied Mathematics Quarterly, Vol.18, No. 2, 395–409, 2022

·Nazarov, The Hormander Proof of the Bourgain–Milman theorem, In: Klartag, B., Mendelson, S., Milman V. (eds), Geometric aspects of functional analysis, Lecture notes in Mathematics Vol. 2050, Springer, 2012.

 

报告人Bojie He (Postdoc)(Peking University)

 On the subadditivity of generalized Kodaira dimensions (Part II)

  126(星期二), 15:30-18:30

  点:腾讯会议:196-467-919

摘 要In these series of talks, we will focus on the study of the Iitaka conjecture, which predicts the subadditivity of Kodaira dimensions for any algebraic fiber space. In the first part, we recall some basic results in the study of Iitaka conjecture and then give an analytic approach to O. Fujino’s result on the subadditivity of the log Kodaira dimensions. In the second part, we introduce the notion of generalized numerical Kodaira dimension with multiplier ideal sheaf and establish subadditive inequalities in terms of this notion. We also recall the definition of generalized Kodaira dimension with multiplier ideal sheaf and then study the Newton-Okounkov body associated to its corresponding graded subalgebra. As an application, we give another proof of Zhou-Zhu’s subadditivity formula of generalized Kodaira dimensions, in the special case when the singular metric with semi-positive curvature current has inf-analytic singularities, by using generalized Iitaka fiberings. This is joint work with Prof. Xiangyu Zhou.

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