数学学科2024系列学术报告之四至六

数学学科2024系列学术报告之四

  报告题目：Extension of multi-valued holomorphic functions on a Stein space

　　报告人：李小山

　　报告时间：5月3日（星期五）16:00-17:00

　　报告地点：理内射白浆一区二区在线观看1-301

　　中文摘要: 最近有两位学者在维数大于等于3且具有紧致强拟凸边界的奇异Stein空间上建立了经典Kerner定理的一个新版本; 同时在维数为2的奇异Stein空间上也得到了部分结果. 我们将证明在完全一般情形下二维奇异Stein空间上剩余的公开问题. 这是与黄孝军教授合作完成的工作. 

　　英文摘要: A version of the classical Kerner's theorem for a singular Stein space with a compact strongly pseudoconvex boundary has been recently established by Huang and Xiao when the dimension of space is greater or equal to three. A partial result for the case of complex dimension two was also obtained by them. In this talk, we will show and answer to the two dimensional case left open in in its full generality. This talk is based on a joint work with Xiaojun Huang.

报告人简介：李小山，武汉大学副教授。主要从事多复变函数论的研究，先后主持国家自然科学基金青年项目1项、面上项目2项、国际（地区）合作与交流项目1项，在Math. Ann.、JFA、TAMS、IMRN、MRL、Math. Z.等国际数学知名期刊发表论文20余篇。 

数学学科2024系列学术报告之五

　　报告题目：Geometric and analytic properties associated with extension operators

　　报告人：王建飞

　　报告时间：5月5日（星期日）9:30-10:30

　　报告地点：理内射白浆一区二区在线观看1-301

　　中文摘要: 我们首先刻画了Roper-Suffridge延拓算子在由凸函数所定义的一般域上保持E-星形性质; 其次构造了Reinhard域上的广义Roper-Sufffridge延拓算子, 并解决了Gong和Liu所提出的一个公开问题; 最后在有界对称域上推广了Pfaltzgraff-Sufffridge延拓算子, 并证明了Loewer链是保持的. 这是与刘太顺教授、张艳慧教授合作完成的工作.

　　英文摘要: In this talk, we first prove that the Roper-Suffridge extension operator preserves E-starlike property on general domains given by convex functions. Next, we construct the generalized Roper-Suffridge extension operator on Reinhard domains which solves a problem of Gong and Liu. Finally, we generalize the Pfaltzgraff-Suffridge extension operator over bounded symmetric domains and prove Loewner chains are preserved. Further, we propose two conjectures. This recent work is joint with Prof. Taishun Liu and Yanhui Zhang. 

报告人简介：王建飞，华侨大学特聘教授，福建省闽江学者特聘教授。主要从事多复变函数论的研究，已在TAMS、J. Geom. Anal.、Pacific J. Math.、中国科学等国内外期刊发表学术论文30余篇，主持国家自然科学基金与省级科研项目多项。

　　报告题目：Proper mappings between indefinite hyperbolic spaces and type I classical domains

　　报告人：卢金

　　报告时间：5月5日（星期日）10:30-11:30

　　报告地点：理内射白浆一区二区在线观看1-301

　　中文摘要: 我们将介绍不定双曲空间之间的映射问题, 推广了Baouendi-Ebenfelt-Huang 和Ng的研究结果; 然后证明了典型域I之间逆紧全纯映射的刚性, 解决了Chan提出并经Zaitsev-Kim、Kim等研究的一个猜想. 

　　英文摘要:  In this talk, we will introduce a mapping problem between indefinite hyperbolic spaces by employing the work established earlier by the authors. In particular, we generalize certain theorems proved by Baouendi-Ebenfelt-Huang and Ng. Then we use these results to prove a rigidity result for proper holomorphic mappings between type I classical domains, which confirms a conjecture formulated by Chan after the work of Zaitsev-Kim, Kim and himself.

　　报告人简介：卢金，安徽大学副教授。主要从事多复变函数论的研究，先后主持、参与国家自然科学基金、省自然科学基金项目近10项，已在Adv.Math.、TAMS、J. Geom. Anal.等国内外期刊发表学术论文近20篇。

数学学科2024系列学术报告之六

　　报告题目：Commutator type and Levi type of a system of CR vector fields

　　报告人：尹万科

　　报告时间：5月6日（星期一）15:30-16:30

　　报告地点：理内射白浆一区二区在线观看1-301

　　中文摘要: 在研究C^n中的拟凸实超曲面时, 自然会产生有限型条件, 被用于测量Levi形式的退化程度. 设M是C^n中的拟凸实超曲面, p是M中的点. 设B是CR切丛T^{(1, 0)}M的子丛. 交换子型t(B, p)是用来测量B中的截面及其共轭作交换子生成点的切触方向的次数. Levi型c(B, p)考虑的是沿着B中的截面及其共轭来区分Levi形式. 人们认为这两种有限型是相同的, 这被称为广义D’Angelo猜想. 我们将介绍这一猜想的最新研究进展. 这是与黄孝军教授和袁平三博士合作完成的工作.

　　英文摘要: Finite type conditions arise naturally during the study of weakly pseudoconvex hypersurfaces in C^n, which are defined to measure to degeneracy of the Levi form. Let M be a pseudoconvex hypersurface in C^n, p\in M, and let B be a subbundle of the CR tangent bundle T^{(1, 0)}M. The commutator type t(B, p) measures the number of commutators of the sections of B and their conjugates needed to generate the contact tangent vector at p. The Levi type c(B, p) is concerned with differentiating the Levi form along the sections of B and their conjugates. It is believed that these two types are the same, which is known as the generalized D’Angelo Conjecture. In this talk, I shall talk about the recent progress on this conjecture, which are joint works with X. Huang and P. Yuan.

　　报告人简介：尹万科，武汉大学教授，2017年国家优青。主要从事多复变函数论的研究，在复欧氏空间实超曲面的若干重要问题上取得了一系列重要进展，研究工作先后发表在 Invent. Math.、Math. Ann.、Adv. Math和J. Math. Pures Appl.等国际知名数学期刊。