召集人：周向宇（中国科学院数学与系统科学研究院）、萧荫堂（Harvard University）、John Erik Fornæss（Norwegian University of Science and Technology）
时间：2024.07.28—2024.08.03
Conference Program
Time: 29th July (Monday) Place: Lecture Hall
08:30-09:00 | Opening remarks & photos |
Talks（Moderator：Prof. Xiangyu Zhou ） | |
09:00-10:00 | Recent developments in multiplier ideal sheaf and jet differentiation techniques Prof. Yum-Tong Siu（Harvard University） |
10:00-10:30 | Tea Break |
10:30-11:30 | Positive scalar curvature on manifolds and foliations Prof. Weiping Zhang（Nankai University） |
11:30-13:00 | Lunch |
Talks（Moderator：Prof. Chunping Zhong/Zehua Zhou/Qingchun Ji ） | |
14:00-15:00 | A general Schwarz lemma for strongly pseudoconvex complex Finsler manifolds Prof. Chunhui Qiu（Xiamen University） |
15:00-15:30 | Tea Break |
15:30-16:30 | Geometric and analytic properties associated with extension operators Prof. Jianfei Wang（Huaqiao University） |
16:45-17:45 | Some recent progress on the Burns-Krantz type rigidity Prof. Feng Rong（Shanghai Jiao Tong University） |
17:45-19:15 | Dinner |
Time: 30th July (Tuesday) Place: Conference Room
Talks（Moderator：Prof. John Erik Fornæss ） | |
09:00-10:00 | K-Theory of Topological Insulators Prof. Armen Sergeev（Steklov Mathematical Institute of Russian Academy of Sciences） |
10:00-10:30 | Tea Break |
10:30-11:30 | Bergman kernels on punctured Riemann surfaces Prof. Xiaonan Ma（Université de Paris） |
11:30-13:00 | Lunch |
Talks（Moderator：Prof. Taishun Liu/Ruicong Wu /Qingchun Ji） | |
14:00-15:00 | The LYZ equation Prof. Jixiang Fu（Fudan University） |
15:00-15:30 | Tea Break |
15:30-16:30 | Results related with complex structures on S6 Prof. Wenjiao Yan（Beijing Normal University） |
16:45-17:45 | Second Main Theorems for Degenerate Holomorphic Curves in the Projective Space Prof. Qiming Yan（Tongji University） |
17:45-19:15 | Dinner |
| Talks Information
n Prof. Yum-Tong Siu（Harvard University） Title：Recent developments in multiplier ideal sheaf and jet differentiation techniques Abstract：In the area of multiplier ideal sheaf and jet differentiation techniques, there are many important active topics of research. For example, the global nondeformability problem for irreducible compact Hermitian symmetric manifolds, effective construction of line bundle sections such as the very ampleness part of the Fujita conjecture, Kohn’s algorithm relating multiplier ideal sheaves to subellipticity estimates in the complex Neumann problem, problems of hyperbolicity and rational points. We will talk about the background, recent results and open problems in some such topics. n Prof. Weiping Zhang（Nankai University） |
Title：Positive scalar curvature on manifolds and foliations Abstract：We describe some advances on problems concerning the existence of metrics of positive scalar curvature on manifolds and foliations. n Prof. Chunhui Qiu（Xiamen University） Title：A general Schwarz lemma for strongly pseudoconvex complex Finsler manifolds Abstract：In this paper, we generalize a Schwarz lemma to strongly pseudoconvex complex Finsler manifolds, and prove a Schwarz lemma between two strongly pseudoconvex complex Finsler manifolds. As an application, we give a rigidity result. This is joint with Jinling Li and Qixin Zhang n Prof. Jianfei Wang（Huaqiao University） Title：Geometric and analytic properties associated with extension operators Abstract：The first part of the talk is to prove that the Roper-Suffridge extension operator preserves E-starlike property on domains given by convex functions. The second is to construct the generalized Roper-Suffridge operator on Reinhard domains. This solves a problem of Gong and Liu. Finally, by obtaining geometric and analytic properties of bounded symmetric domains, we generalize the Pfaltzgraff-Suffridge extension operator over bounded symmetric domains and prove Loewner chains are also preserved with a new idea. Further, we propose two conjectures for convexity property. n Prof. Feng Rong（Shanghai Jiao Tong University） Title：Some recent progress on the Burns-Krantz type rigidity Abstract：We will report on some of our recent results on the Burns-Krantz type rigidity, such as rigidity on fibered domains, rigidity on domains with corners, and the proof of Huang's conjecture. Some of the work are joint with John Erik Fornaess, and with Sui-Chung Ng. |
n Prof. Armen Sergeev（Steklov Mathematical Institute of Russian Academy of Sciences） Title：K-Theory of Topological Insulators Abstract：Topological insulators are the solid bodies with a broad energy gap stable under small deformations. It motivates the usage of the topological methods in their investigation. To quantize the theory of topological insulators we reformulate it in the language of K-theory. To do that we note that the algebra of observables of the topological insulators belongs to the class of graded C*-algebras for which there is a variant of K-theory proposed by Van Daele. In terms of this theory it is possible to define also the topological invariants of insulators. A key role in the investigation of the topological properties of solid bodies is played by the study of their symmetry groups. Kitaev has proposed a description of symmetries and classification of solid bodies based on the theory of Clifford algebras. In this way the quantization of the theory of topological insulators is reduced to the study of irreducible representations of Clifford algebras. This quantization construction works in the bulk of the insulator, however at its boundary the energy gap which is necessary for the K-theory construction in the bulk may close at the boundary. To describe the arising gapless system we have to use another variant of K-theory proposed by Kasparov. In its terms it is possible to describe the algebra of the boundary observables and define the boundary topological invariants of insulators. A relation between the topological invariants of the insulator and its boundary is established by the so called BB-correspondence. For its construction it is used a short exact sequence connecting the algebras of observables of the insulator and its boundary. It generates the long exact sequence of homomorphisms of K-groups such that the BB-correspondence coincides with the boundary map in this sequence. The study was carried out with the financial support of the Ministry of Science and Higher Education of the Russian Federation in the framework of a scientific project under agreement No. 075-15-2024-631.
n Prof. Xiaonan Ma（Université de Paris） |
Title：Bergman kernels on punctured Riemann surfaces Abstract：We will review our recent works on Bergman kernel on punctured Riemann surfaces. We consider a punctured Riemann surface endowed with a Hermitian metric that equals the Poincaré metric near the punctures, and a holomorphic line bundle that polarizes the metric. We will explain the Bergman kernel can be localized around the singularities and its local model is the Bergman kernel of the punctured unit disc endowed with the standard Poincaré metric. We will explain that the quotient of the Bergman kernel of high tensor powers of the line bundle and of the Bergman kernel of the Poincaré model near the singularity tends to one up to arbitrary negative powers of the tensor power. This is a joint work with Hugues Auvray and George Marinescu. n Prof. Jixiang Fu（Fudan University） Title：The LYZ equation Abstract：The LYZ equation is also called the deformed Hermitian Yang-Mills equation in literature. In this talk we first recall the recent progress of the LYZ equation, and then introduce a new flow solving the LYZ equation in Kahler geometry. This is a joint work with S.-T. Yau and Dekai Zhang. n Prof. Wenjiao Yan（Beijing Normal University） Title：Results related with complex structures on S6 Abstract：It is a longstanding problem that whether there exists a complex structure on the 6-dimensional sphere? Many famous mathematicians have made efforts on this problem, such as Hopf, Wen-tsun Wu, Borel, Serre, LeBrun, Shiing-Shen Chern, Atiyah, etc. This talk consists of two parts. (i) Taking advantage of isoparametric theory, we construct complex structures on certain isoparametric hypersurfaces in the unit sphere. As a consequence, there is a closed 8-dimensional manifold N8 such that there exists a complex structure on S6 X N8. (ii) As a generalization of LeBrun's result, we prove that there is no orthogonal almost complex structure on the standard S6 with the length of Nijenhuis tensor smaller than a certain constant everywhere. This talk is based on joint works with Professor Zizhou Tang.
n Prof. Qiming Yan（Tongji University） Title：Second Main Theorems for Degenerate Holomorphic Curves in the Projective Space Abstract：In this talk, we will introduce some second main theorems for degenerate holomorphic curves in $\mathbb{P}^n$ with hypersurfaces and moving hypersurfaces. This is based on the joint works with Lei Shi and Guangsheng Yu. |
参会人员名单
| 姓名 | 工作单位 |
| Yum-Tong Siu | 哈佛大学 |
| 张伟平 | 南开大学 |
| 周向宇 | 中科院数学与系统科学研究院 |
| Armen Sergeev | 俄罗斯科学院斯捷克洛夫数学研究所 |
| Takeo OHSAWA | Nagoya University |
| Siqi Fu | Rutgers University-Camden |
| Ma Xiaonan | Université de Paris |
| John Erik Fornæss | 挪威科技大学 |
| 钱涛 | 澳门科技大学 |
| 关启安 | 北京大学 |
| 彦文娇 | 北京师范大学 |
| 汪志威 | 北京师范大学 |
| 嵇庆春 | 复旦大学 |
| 傅吉祥 | 复旦大学 |
| 仝策中 | 河北工业大学 |
| 乔玉英 | 河北师范大学 |
| 刘太顺 | 湖州师范学院 |
| 吴瑞聪 | 华东师范大学 |
| 王建飞 | 华侨大学 |
| 程晓亮 | 吉林师范大学 |
| 邱春晖 | 厦门大学 |
| 钟春平 | 厦门大学 |
| 戎锋 | 上海交通大学 |
| 张文俊 | 深圳大学 |
| 张利友 | 首都师范大学 |
| 王安 | 首都师范大学 |
| 周泽华 | 天津大学 |
| 颜启明 | 同济大学 |
| 涂振汉 | 武汉大学 |
| 饶胜 | 武汉大学 |
| 尹万科 | 武汉大学 |
| 朱朗峰 | 武汉大学 |
| 王伟 | 浙江大学 |
| 刘聪文 | 中国科技大学 |
| 任广斌 | 中国科技大学 |
| 邓富声 | 中国科学院大学 |
| 万学远 | 重庆理工大学 |
| 刘劲松 | 中科院数学与系统科学研究院 |
| 谢松晏 | 中科院数学与系统科学研究院 |
| 高洁欣 | 澳门大学 |
| 孟宪奎 | 北京邮电大学 |
| 姚莎 | 河南理工大学 |
| 李军 | 湖南大学 |
| 李震乾 | 湘潭大学 |
| 宁家福 | 中南大学 |
| 吴菊杰 | 中山大学珠海校区 |
| 邵国宽 | 中山大学珠海校区 |
| 林章立 | 厦门大学 |
| 李植 | 北京邮电大学 |
| 徐旺 | 中山大学 |