數(shù)學(xué)學(xué)科2024系列學(xué)術(shù)報(bào)告之四

  報(bào)告題目：Extension of multi-valued holomorphic functions on a Stein space

　　報(bào)告人：李小山

　　報(bào)告時(shí)間：5月3日（星期五）16:00-17:00

　　報(bào)告地點(diǎn)：理學(xué)院1-301

　　中文摘要: 最近有兩位學(xué)者在維數(shù)大于等于3且具有緊致強(qiáng)擬凸邊界的奇異Stein空間上建立了經(jīng)典Kerner定理的一個(gè)新版本; 同時(shí)在維數(shù)為2的奇異Stein空間上也得到了部分結(jié)果. 我們將證明在完全一般情形下二維奇異Stein空間上剩余的公開問題. 這是與黃孝軍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.

報(bào)告人簡介：李小山,，武漢大學(xué)副教授。主要從事多復(fù)變函數(shù)論的研究，先后主持國家自然科學(xué)基金青年項(xiàng)目1項(xiàng)、面上項(xiàng)目2項(xiàng)、國際（地區(qū)）合作與交流項(xiàng)目1項(xiàng),，在Math. Ann.、JFA,、TAMS,、IMRN、MRL,、Math. Z.等國際數(shù)學(xué)知名期刊發(fā)表論文20余篇,。 

數(shù)學(xué)學(xué)科2024系列學(xué)術(shù)報(bào)告之五

　　報(bào)告題目：Geometric and analytic properties associated with extension operators

　　報(bào)告人：王建飛

　　報(bào)告時(shí)間：5月5日（星期日）9:30-10:30

　　報(bào)告地點(diǎn)：理學(xué)院1-301

　　中文摘要: 我們首先刻畫了Roper-Suffridge延拓算子在由凸函數(shù)所定義的一般域上保持E-星形性質(zhì); 其次構(gòu)造了Reinhard域上的廣義Roper-Sufffridge延拓算子, 并解決了Gong和Liu所提出的一個(gè)公開問題; 最后在有界對(duì)稱域上推廣了Pfaltzgraff-Sufffridge延拓算子, 并證明了Loewer鏈?zhǔn)潜３值?/span>. 這是與劉太順教授、張艷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. 

報(bào)告人簡介：王建飛，華僑大學(xué)特聘教授,，福建省閩江學(xué)者特聘教授,。主要從事多復(fù)變函數(shù)論的研究，已在TAMS,、J. Geom. Anal.,、Pacific J. Math.、中國科學(xué)等國內(nèi)外期刊發(fā)表學(xué)術(shù)論文30余篇,，主持國家自然科學(xué)基金與省級(jí)科研項(xiàng)目多項(xiàng),。

　　報(bào)告題目：Proper mappings between indefinite hyperbolic spaces and type I classical domains

　　報(bào)告人：盧金

　　報(bào)告時(shí)間：5月5日（星期日）10:30-11:30

　　報(bào)告地點(diǎn)：理學(xué)院1-301

　　中文摘要: 我們將介紹不定雙曲空間之間的映射問題, 推廣了Baouendi-Ebenfelt-Huang 和Ng的研究結(jié)果; 然后證明了典型域I之間逆緊全純映射的剛性, 解決了Chan提出并經(jīng)Zaitsev-Kim、Kim等研究的一個(gè)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.

　　報(bào)告人簡介：盧金,，安徽大學(xué)副教授,。主要從事多復(fù)變函數(shù)論的研究，先后主持,、參與國家自然科學(xué)基金,、省自然科學(xué)基金項(xiàng)目近10項(xiàng)，已在Adv.Math.,、TAMS、J. Geom. Anal.等國內(nèi)外期刊發(fā)表學(xué)術(shù)論文近20篇,。

數(shù)學(xué)學(xué)科2024系列學(xué)術(shù)報(bào)告之六

　　報(bào)告題目：Commutator type and Levi type of a system of CR vector fields

　　報(bào)告人：尹萬科

　　報(bào)告時(shí)間：5月6日（星期一）15:30-16:30

　　報(bào)告地點(diǎn)：理學(xué)院1-301

　　中文摘要: 在研究C^n中的擬凸實(shí)超曲面時(shí), 自然會(huì)產(chǎn)生有限型條件, 被用于測量Levi形式的退化程度. 設(shè)M是C^n中的擬凸實(shí)超曲面, p是M中的點(diǎn). 設(shè)B是CR切叢T^{(1, 0)}M的子叢. 交換子型t(B, p)是用來測量B中的截面及其共軛作交換子生成點(diǎn)的切觸方向的次數(shù). Levi型c(B, p)考慮的是沿著B中的截面及其共軛來區(qū)分Levi形式. 人們認(rèn)為這兩種有限型是相同的, 這被稱為廣義D’Angelo猜想. 我們將介紹這一猜想的最新研究進(jìn)展. 這是與黃孝軍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.

　　報(bào)告人簡介：尹萬科,，武漢大學(xué)教授，2017年國家優(yōu)青,。主要從事多復(fù)變函數(shù)論的研究,，在復(fù)歐氏空間實(shí)超曲面的若干重要問題上取得了一系列重要進(jìn)展，研究工作先后發(fā)表在 Invent. Math.,、Math. Ann.,、Adv. Math和J. Math. Pures Appl.等國際知名數(shù)學(xué)期刊。