[geometry-ml:06049] 岡数学研究所セミナ−のご案内

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松澤淳一
〒630-8506 奈良市北魚屋西町
奈良女子大学　岡数学研究所　
Phone: 0742-20-3361 (研究室)
FAX: 0742-20-3367 (事務室）
matsuzawa ＠ cc.nara-wu.ac.jp

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Seminar in Oka Mathematical Institute

Date:    December 12th, Thursday, 2024
Place:   Room B1406, B Hall (Faculty Science) , Nara Women's University

Speakers and Titles

10:00—10:50
Takayuki Koike (Osaka Metropolitan University)
Formal principle for holomorphic line bundles and its application

11:00—11:50
Laurent Stolovitch (Université Côte d'Azur)
CR singularities and dynamical systems

12:00—12:50
Tohru Morimoto (Oka Mathematical Institute)
Nilpotent analysis and geometry of differential equations on filtered manifolds

Abstract

T. Koike
We investigate the formal principle for holomorphic line bundles on neighborhoods of an analytic subset of a complex manifold, mainly when it can be realized as an open subset of a compact Kahler manifold. We also discuss its application to some problems in complex geometry. 

L. Stolobitch
In this talk, we'll survey some recent results done since the seminal work of Moser and Webster about smooth real analytic surfaces in $C^2$ which 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 of these surface near the 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.

 T. Morimoto
In this talk we ask a question whether there exists a solution to an arbitrary given system of non-linear differential equations on a filtered manifold. Then we give an outline of the general theory which answer the question above.The theory consists of three parts:  (I) Criterion for the existence of formal solutions, (II) Existence of formal Gevrey solutions, (III) Existence of analytic solutions. In particular, we obtain an existence theorem of local analytic solutions to a large class of systems of non-linear partial differential equations with singularities. We will discuss also the equivalence problems (and the invariants) of differential equations on filtered manifolds of finite type, linear and non-linear, respectively as the equivalence problem of extrinsic geometry and intrinsic geometry, as well as mutual interesting relations between them.
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