## Seminar on Geometric Complex Analysis

Seminar information archive ～12/08｜Next seminar｜Future seminars 12/09～

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**

### 2017/01/16

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

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.)

(JAPANESE)

**Yu Kawakami**(Kanazawa University)(JAPANESE)

### 2016/12/05

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Takahiro Oba**(Tokyo Institute of Technology )(JAPANESE)

### 2016/11/28

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Satoshi Nakamura**(Tohoku University)(JAPANESE)

### 2016/11/21

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Toshihiro Nose**(Fukuoka Institute of Technology)(JAPANESE)

### 2016/11/14

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Sachiko Hamano**(Osaka City University)(JAPANESE)

### 2016/11/07

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Hideyuki Ishi**(Nagoya University)(JAPANESE)

### 2016/10/31

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Yutaka Ishii**(Kyushu University)(JAPANESE)

### 2016/10/24

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

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.)

(JAPANESE)

**Takaaki Nomura**(Kyushu University)(JAPANESE)

### 2016/10/03

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

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.)

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.)

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.)

(JAPANESE)

**Masanori Adachi**(Tokyo University of Science)(JAPANESE)

### 2016/06/06

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Shin Kikuta**(Kogakuin University)(JAPANESE)

### 2016/05/30

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Takeo Ohsawa**(Nagoya University)(JAPANESE)

### 2016/05/23

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

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.)

(JAPANESE)

**Masataka Tomari**(Nihon University)(JAPANESE)

### 2016/05/09

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

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.)

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.)

(JAPANESE)

**Kunio Obitsu**(Kagoshima University)(JAPANESE)

### 2016/04/11

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

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.)

(Japanese)

**Kunio Obitsu**(Kagoshima Univ.)(Japanese)

### 2016/01/18

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Holomorphic motions and the monodromy (Japanese)

**Hiroshige Shiga**(Tokyo Institute of Technology)Holomorphic motions and the monodromy (Japanese)

[ Abstract ]

Holomorphic motions, which was introduced by Mane, Sad and Sullivan, is a useful tool for Teichmuller theory as well as for complex dynamics. In particular, Slodkowski’s theorem makes a significant contribution to them. The theorem says that every holomorphic motion of a closed set on the Riemann sphere parametrized by the unit disk is extended to a holomorphic motion of the whole Riemann sphere parametrized by the unit disk. In this talk, we consider a generalization of the theorem. If time permits, we will discuss applications of our results.

Holomorphic motions, which was introduced by Mane, Sad and Sullivan, is a useful tool for Teichmuller theory as well as for complex dynamics. In particular, Slodkowski’s theorem makes a significant contribution to them. The theorem says that every holomorphic motion of a closed set on the Riemann sphere parametrized by the unit disk is extended to a holomorphic motion of the whole Riemann sphere parametrized by the unit disk. In this talk, we consider a generalization of the theorem. If time permits, we will discuss applications of our results.

### 2015/12/21

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On pseudo Kobayashi hyperbolicity of subvarieties of abelian varieties

(Japanese)

**Katsutoshi Yamanoi**(Osaka Univ.)On pseudo Kobayashi hyperbolicity of subvarieties of abelian varieties

(Japanese)

[ Abstract ]

A subvariety of an abelian variety is of general type if and only if it is pseudo Kobayashi hyperbolic. I will discuss the proof of this result.

A subvariety of an abelian variety is of general type if and only if it is pseudo Kobayashi hyperbolic. I will discuss the proof of this result.