Seminar on Geometric Complex Analysis
Seminar information archive ~04/17|Next seminar|Future seminars 04/18~
Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
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Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
Seminar information archive
2017/02/13
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Qi'an Guan (Peking University)
A Characterization of regular points by Ohsawa-Takegoshi Extension Theorem (ENGLISH)
Qi'an Guan (Peking University)
A Characterization of regular points by Ohsawa-Takegoshi Extension Theorem (ENGLISH)
[ Abstract ]
In this talk, we will present that the germ of a complex analytic set at the origin in $\mathbb{C}^n$ is regular if and only if the related Ohsawa-Takegoshi extension theorem holds. We also present a necessary condition of the $L^2$ extension of bounded holomorphic sections from singular analytic sets.
This is joint work with Dr. Zhenqian Li.
In this talk, we will present that the germ of a complex analytic set at the origin in $\mathbb{C}^n$ is regular if and only if the related Ohsawa-Takegoshi extension theorem holds. We also present a necessary condition of the $L^2$ extension of bounded holomorphic sections from singular analytic sets.
This is joint work with Dr. Zhenqian Li.
2017/01/23
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Junjiro Noguchi (The University of Tokyo)
A unified proof of Cousin I, II and d-bar equation on domains of holomorphy (JAPANESE)
Junjiro Noguchi (The University of Tokyo)
A unified proof of Cousin I, II and d-bar equation on domains of holomorphy (JAPANESE)
[ Abstract ]
Oka's J\^oku-Ik\^o says that holomorphic functions on a complex submanifold of a polydisk extend holomorphically to the whole polydisk. By making use of Oka's J\^oku-Ik\^o we give a titled proof with introducing an argument that represents one of the three cases.
The proof is a modification of the cube dimension induction, used in the proof of Oka's Syzygy for coherent sheaves.
Oka's J\^oku-Ik\^o says that holomorphic functions on a complex submanifold of a polydisk extend holomorphically to the whole polydisk. By making use of Oka's J\^oku-Ik\^o we give a titled proof with introducing an argument that represents one of the three cases.
The proof is a modification of the cube dimension induction, used in the proof of Oka's Syzygy for coherent sheaves.
2017/01/16
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Dinh Tuan Huynh (Osaka University)
A geometric second main theorem (ENGLISH)
Dinh Tuan Huynh (Osaka University)
A geometric second main theorem (ENGLISH)
[ Abstract ]
Using Ahlfors’ theory of covering surfaces, we establish a Cartan’s type Second Main Theorem in the complex projective plane with 1–truncated counting functions for entire holomorphic curves which cluster on an algebraic curve.
Using Ahlfors’ theory of covering surfaces, we establish a Cartan’s type Second Main Theorem in the complex projective plane with 1–truncated counting functions for entire holomorphic curves which cluster on an algebraic curve.
2016/12/12
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yu Kawakami (Kanazawa University)
(JAPANESE)
Yu Kawakami (Kanazawa University)
(JAPANESE)
2016/12/05
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takahiro Oba (Tokyo Institute of Technology )
(JAPANESE)
Takahiro Oba (Tokyo Institute of Technology )
(JAPANESE)
2016/11/28
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Satoshi Nakamura (Tohoku University)
(JAPANESE)
Satoshi Nakamura (Tohoku University)
(JAPANESE)
2016/11/21
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Toshihiro Nose (Fukuoka Institute of Technology)
(JAPANESE)
Toshihiro Nose (Fukuoka Institute of Technology)
(JAPANESE)
2016/11/14
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Sachiko Hamano (Osaka City University)
(JAPANESE)
Sachiko Hamano (Osaka City University)
(JAPANESE)
2016/11/07
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hideyuki Ishi (Nagoya University)
(JAPANESE)
Hideyuki Ishi (Nagoya University)
(JAPANESE)
2016/10/31
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yutaka Ishii (Kyushu University)
(JAPANESE)
Yutaka Ishii (Kyushu University)
(JAPANESE)
2016/10/24
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Satoru Shimizu (Tohoku University)
Structure and equivalence of a class of tube domains with solvable groups of automorphisms (JAPANESE)
Satoru Shimizu (Tohoku University)
Structure and equivalence of a class of tube domains with solvable groups of automorphisms (JAPANESE)
[ Abstract ]
In the study of the holomorphic equivalence problem for tube domains, it is fundamental to investigate tube domains with polynomial infinitesimal automorphisms. To apply Lie group theory to the holomorphic equivalence problem for such tube domains $T_\Omega$, investigating certain solvable subalgebras of $\frak g(T_{\Omega})$ plays an important role, where $\frak g(T_{\Omega})$ is the Lie algebra of all complete polynomial vector fields on $T_\Omega$. Related to this theme, we discuss the structure and equivalence of a class of tube domains with solvable groups of automorphisms. Besides, we give a concrete example of a tube domain whose automorphism group is solvable and contains nonaffine automorphisms.
In the study of the holomorphic equivalence problem for tube domains, it is fundamental to investigate tube domains with polynomial infinitesimal automorphisms. To apply Lie group theory to the holomorphic equivalence problem for such tube domains $T_\Omega$, investigating certain solvable subalgebras of $\frak g(T_{\Omega})$ plays an important role, where $\frak g(T_{\Omega})$ is the Lie algebra of all complete polynomial vector fields on $T_\Omega$. Related to this theme, we discuss the structure and equivalence of a class of tube domains with solvable groups of automorphisms. Besides, we give a concrete example of a tube domain whose automorphism group is solvable and contains nonaffine automorphisms.
2016/10/17
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takaaki Nomura (Kyushu University)
(JAPANESE)
Takaaki Nomura (Kyushu University)
(JAPANESE)
2016/10/03
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hirokazu Shimauchi (Yamanashi Eiwa College)
Visualizing the radial Loewner flow and the evolution family (JAPANESE)
Hirokazu Shimauchi (Yamanashi Eiwa College)
Visualizing the radial Loewner flow and the evolution family (JAPANESE)
2016/06/27
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takayuki Koike (Kyoto University)
On a higher codimensional analogue of Ueda theory and its applications (JAPANESE)
Takayuki Koike (Kyoto University)
On a higher codimensional analogue of Ueda theory and its applications (JAPANESE)
[ Abstract ]
Let $Y$ be a compact complex manifold embedded in a complex manifold with unitary flat normal bundle. As a higher-codimensional generalization of Ueda's theory, we investigate the analytic structure of a neighborhood of $Y$. As an application, we give a criterion for the existence of a smooth Hermitian metric with semi-positive curvature on a nef line bundle.
Let $Y$ be a compact complex manifold embedded in a complex manifold with unitary flat normal bundle. As a higher-codimensional generalization of Ueda's theory, we investigate the analytic structure of a neighborhood of $Y$. As an application, we give a criterion for the existence of a smooth Hermitian metric with semi-positive curvature on a nef line bundle.
2016/06/20
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shin-ichi Matsumura (Tohoku University)
A transcendental approach to injectivity theorems for log canonical pairs (JAPANESE)
Shin-ichi Matsumura (Tohoku University)
A transcendental approach to injectivity theorems for log canonical pairs (JAPANESE)
2016/06/13
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Masanori Adachi (Tokyo University of Science)
(JAPANESE)
Masanori Adachi (Tokyo University of Science)
(JAPANESE)
2016/06/06
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shin Kikuta (Kogakuin University)
(JAPANESE)
Shin Kikuta (Kogakuin University)
(JAPANESE)
2016/05/30
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takeo Ohsawa (Nagoya University)
(JAPANESE)
Takeo Ohsawa (Nagoya University)
(JAPANESE)
2016/05/23
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Katsusuke Nabeshima (The University of Tokushima)
A computation method for algebraic local cohomology and its applications (JAPANESE)
Katsusuke Nabeshima (The University of Tokushima)
A computation method for algebraic local cohomology and its applications (JAPANESE)
[ Abstract ]
Local cohomology was introduced by A. Grothendieck. Subsequent development to a great extent has been motivated by Grothendieck's ideas. Nowadays, local cohomology is a key ingredient in algebraic geometry, commutative algebra, topology and D-modules, and is a fundamental tool for applications in several fields.
In this talk, an algorithmic method to compute algebraic local cohomology classes (with parameters), supported at a point, associated with a given zero-dimensional ideal, is considered in the context of symbolic computation. There are several applications of the method. For example, the method can be used to analyze properties of singularities and deformations of Artin algebra. As the applications, methods for computing standard bases of zero-dimensional ideals and solving ideal membership problems, are also introduced.
Local cohomology was introduced by A. Grothendieck. Subsequent development to a great extent has been motivated by Grothendieck's ideas. Nowadays, local cohomology is a key ingredient in algebraic geometry, commutative algebra, topology and D-modules, and is a fundamental tool for applications in several fields.
In this talk, an algorithmic method to compute algebraic local cohomology classes (with parameters), supported at a point, associated with a given zero-dimensional ideal, is considered in the context of symbolic computation. There are several applications of the method. For example, the method can be used to analyze properties of singularities and deformations of Artin algebra. As the applications, methods for computing standard bases of zero-dimensional ideals and solving ideal membership problems, are also introduced.
2016/05/16
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Masataka Tomari (Nihon University)
(JAPANESE)
Masataka Tomari (Nihon University)
(JAPANESE)
2016/05/09
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Atsushi Atsuji (Keio University)
Nevanlinna type theorems for meromorphic functions on negatively curved Kähler manifolds (JAPANESE)
Atsushi Atsuji (Keio University)
Nevanlinna type theorems for meromorphic functions on negatively curved Kähler manifolds (JAPANESE)
[ Abstract ]
We discuss a generalization of classical Nevanlinna theory to meromorphic functions on complete Kähler manifolds. Several generalization of domains of functions are known in Nevanlinna theory, especially the results due to W.Stoll are well-known. In general Kähler case the remainder term of the second main theorem of Nevanlinna theory usually takes a complicated form. It seems that we have to modify classical
methods in order to simplify the second main theorem. We will use heat diffusion to do that and show some defect relations. We would also like to give some Liouville type theorems for holomorphic maps by using similar heat diffusion methods.
We discuss a generalization of classical Nevanlinna theory to meromorphic functions on complete Kähler manifolds. Several generalization of domains of functions are known in Nevanlinna theory, especially the results due to W.Stoll are well-known. In general Kähler case the remainder term of the second main theorem of Nevanlinna theory usually takes a complicated form. It seems that we have to modify classical
methods in order to simplify the second main theorem. We will use heat diffusion to do that and show some defect relations. We would also like to give some Liouville type theorems for holomorphic maps by using similar heat diffusion methods.
2016/04/25
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Atsushi Yamamori (Academia Sinica)
The representative domain and its applications (JAPANESE)
Atsushi Yamamori (Academia Sinica)
The representative domain and its applications (JAPANESE)
[ Abstract ]
Bergman introduced the notion of a representative domain to choose a nice holomorphic equivalence class of domains. In this talk, I will explain that the representative domain is also useful to obtain an analogue of Cartan's linearity theorem for some special class of domains.
Bergman introduced the notion of a representative domain to choose a nice holomorphic equivalence class of domains. In this talk, I will explain that the representative domain is also useful to obtain an analogue of Cartan's linearity theorem for some special class of domains.
2016/04/18
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Kunio Obitsu (Kagoshima University)
(JAPANESE)
Kunio Obitsu (Kagoshima University)
(JAPANESE)
2016/04/11
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Taro Asuke (The University of Tokyo)
Defining the Julia sets on CP^2 (JAPANESE)
Taro Asuke (The University of Tokyo)
Defining the Julia sets on CP^2 (JAPANESE)
[ Abstract ]
The Julia sets play a central role in the study of complex dynamical systems as well as Kleinian groups where they appear as limit sets. They are also known to be meaningful for complex foliations without singularities, however still not defined for singular ones. In this talk, I will discuss some expected properties of the Julia sets for singular foliations and difficulties for defining them.
The Julia sets play a central role in the study of complex dynamical systems as well as Kleinian groups where they appear as limit sets. They are also known to be meaningful for complex foliations without singularities, however still not defined for singular ones. In this talk, I will discuss some expected properties of the Julia sets for singular foliations and difficulties for defining them.
2016/01/25
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Kunio Obitsu (Kagoshima Univ.)
(Japanese)
Kunio Obitsu (Kagoshima Univ.)
(Japanese)