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：福利院免费体检区200入口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。
