数学研究所
中国科学院华罗庚数学重点实验室
学术报告
多复变与复几何研讨班
SCV&CG Seminar
Speaker: Prof. Laurent Stolovitch(CNRS and Université Côte d'Azur)
Inviter: 周向宇 院士
Language: English
Title: Recents results on equivalence of neighborhoods of embedded compact complex manifolds and higher codimension foliations
Time&Venue: 2025年3月30日（星期日） 19:00-20:00 & 南楼N913
Abstract: In this talk, we will survey recent works done in collaboration with Xianghong Gong, Takayuki Koike, Xiaojun Wu. We consider an embedded n-dimensional compact complex manifold C in (n+d)-dimensional complex manifolds. We are interested in the holomorphic classification of neighborhoods when the normal bundle is flat.
We will give conditions ensuring that a neighborhood of C in M is biholomorphic to a neighborhood of the zero section of its normal bundle. We also give conditions ensuring the existence of a holomorphic foliation in a neighborhood of C in M having C as a compact leaf, extending Ueda's theory to the higher dimension and codimension cases. Both problems appear as a kind "linearization problem" involving appropriate notions of resonances and small divisors condition.
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Title: CR singularities and dynamical systems
Time&Venue: 2025年4月1日（星期二） 19:00-20:00 & 南楼N913
Abstract:In this talk, we'll survey some recent results done since the seminal work of Moser and Webster about smooth real analytic surfaces in C2which are totally real everywhere but at a point where the tangent space is a complex line. Such a point is called a singularity of the Cauchy-Riemann structure. We are interested in the holomorphic classification and the geometry of these surfaces near this singularity. It happens that there is a deep connection with holomorphic classification of some holomorphic dynamical systems near a fixed point so that new results for the later provide new result for the former.
