Finite type conditions of weakly pseudoconvex hypersurfaces

发布时间：2025-03-14 作者：浏览次数：

Speaker:	尹万科	DateTime:	2025年3月21日（周五）上午10:00-11:00
Brief Introduction to Speaker: 尹万科，武汉大学教授，在Invent. Math. J. Math. Pures Appl., IMRN,, Adv. Math., Math. Ann. 等顶尖杂志上发表过文章, 获得过国家优秀青年基金资助与湖北省自然科学一等奖。		Place:	国交2号楼201
Abstract:Finite type conditions arise naturally during the study of weakly pseudoconvex hypersurfaces in $\mathbb{C}^n$, which are defined to measure to degeneracy of the Levi form. Let $M$ be a pseudoconvex hypersurface in $\mathbb{C}^n$, $p\in M$, 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 ofthe 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 isbased on the joint works with X. Huang and P. Yuan.