## Seminar on Geometric Complex Analysis

Seminar information archive ～08/07｜Next seminar｜Future seminars 08/08～

Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
---|---|

Organizer(s) | Kengo Hirachi, Shigeharu Takayama |

**Seminar information archive**

### 2007/04/23

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

Generalization of Q-curvature in CR geometry

**平地健吾**(東京大学)Generalization of Q-curvature in CR geometry

### 2007/04/16

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

Joyce計量のツイスター空間の具体的な構成方法

**本多 宣博**(東京工業大学)Joyce計量のツイスター空間の具体的な構成方法

### 2007/01/29

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

Radial cluster set of a bounded holomorphic map in the unit ball of C^n

**松島敏夫**(石川工業高専)Radial cluster set of a bounded holomorphic map in the unit ball of C^n

### 2007/01/22

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

Omori-Yau generalized maximum principle

**Hanjin Lee**(Seoul National University)Omori-Yau generalized maximum principle

### 2007/01/15

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

Lagragian constructions for various topological invariants of algebraic varieties (東大数理、松井優氏との共同研究)

**竹内 潔**(筑波大学数理物質科学研究科)Lagragian constructions for various topological invariants of algebraic varieties (東大数理、松井優氏との共同研究)

### 2006/12/18

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

Height functions and affine space regular automorphisms

**川口 周**(京都大学大学院理学研究科)Height functions and affine space regular automorphisms

### 2006/12/11

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

Modified deficiencies of holomorphic curves and defect relation

**相原義弘**(沼津高専)Modified deficiencies of holomorphic curves and defect relation

### 2006/12/04

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

Invariant CR-Laplacian type operator on the Silov boundary of a Siegel domain of rank one

**伊師英之**(横浜市立大学)Invariant CR-Laplacian type operator on the Silov boundary of a Siegel domain of rank one

### 2006/11/27

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

Logarithmic connections along Saito free divisors

**Aleksandr G. Aleksandrov**(Institute for Control Sciences, Moscow)Logarithmic connections along Saito free divisors

[ Abstract ]

We develop an approach to the study of meromorphic connections with logarithmic poles along a Saito free divisor. In particular, basic properties of Christoffel symbols of such connections are established. We also compute the set of all integrable meromorphic connections with logarithmic poles and describe the corresponding spaces of horizontal sections for some examples of Saito free divisors including the discriminants of the minimal versal deformations of $A_2$- and of $A_3$-singularities, and a divisor in $\mathbf{C}^3$ which appeared in a work of M. Sato in the context of the theory of prehomogeneous spaces.

We develop an approach to the study of meromorphic connections with logarithmic poles along a Saito free divisor. In particular, basic properties of Christoffel symbols of such connections are established. We also compute the set of all integrable meromorphic connections with logarithmic poles and describe the corresponding spaces of horizontal sections for some examples of Saito free divisors including the discriminants of the minimal versal deformations of $A_2$- and of $A_3$-singularities, and a divisor in $\mathbf{C}^3$ which appeared in a work of M. Sato in the context of the theory of prehomogeneous spaces.

### 2006/11/20

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

Advances and examples in the value distribution theory

**野口潤次郎**(東大数理)Advances and examples in the value distribution theory

### 2006/11/13

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

Sasaki-Futaki invariant and existence of Einstein metrics on toric Sasaki manifolds

**小野 肇**(東京工業大学)Sasaki-Futaki invariant and existence of Einstein metrics on toric Sasaki manifolds

### 2006/11/06

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

On the extension of twisted pluricanonical forms

**Mihai Paun**(Université Henri Poincaré Nancy)On the extension of twisted pluricanonical forms

### 2006/10/23

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

Classification of hypersurface simple K3 singularities -- 95 and others

**泊 昌孝**(日本大学文理学部)Classification of hypersurface simple K3 singularities -- 95 and others

### 2006/10/16

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

Differentiability of the volume of divisors and Khovanskii-Teissier inequalities

**Sebastien Boucksom**(東大数理 JSPS研究員)Differentiability of the volume of divisors and Khovanskii-Teissier inequalities

### 2006/07/10

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

Characterization of domains in $C^n$ by their noncompact automorphism groups

**Do Duc Thai**(Hanoi教育大)Characterization of domains in $C^n$ by their noncompact automorphism groups

[ Abstract ]

In this talk, the characterization of domains in $C^n$ by their noncompact automorphism groups are given. By this characterization, the Bedford-Pinchuk theorem is true for any domain (not necessary bounded) in $C^n$.

In this talk, the characterization of domains in $C^n$ by their noncompact automorphism groups are given. By this characterization, the Bedford-Pinchuk theorem is true for any domain (not necessary bounded) in $C^n$.

### 2006/07/03

14:00-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Complex Semi-Abelian Varieties II --- Compactifications and etc.

**Jörg Winkelmann**(Université Henri Poincaré Nancy)Complex Semi-Abelian Varieties II --- Compactifications and etc.

### 2006/06/26

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

Toward construction of Green current for modular cycles in modular varieties

**織田孝幸**(東大数理)Toward construction of Green current for modular cycles in modular varieties

### 2006/06/19

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

Deformations and smoothing of (generalized) holomorphic symplectic structures

**後藤竜司**(大阪大学)Deformations and smoothing of (generalized) holomorphic symplectic structures

### 2006/06/12

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

The Rumin complex and Hamiltonian mechanism

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~hirachi/scv/akahori.pdf

**赤堀隆夫**(兵庫県立大学)The Rumin complex and Hamiltonian mechanism

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~hirachi/scv/akahori.pdf

### 2006/06/05

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

Integral formulas for infinite dimensional domains with arbitrary boundary

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~hirachi/scv/Bauer.pdf

**Wolfram Bauer**(東京理科大)Integral formulas for infinite dimensional domains with arbitrary boundary

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~hirachi/scv/Bauer.pdf

### 2006/05/29

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

Uniformisation of Holomorphic Foliations by Curves II

**Marco Brunella**(Bourgogne)Uniformisation of Holomorphic Foliations by Curves II

### 2006/05/29

13:30-15:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Hodge theory with bounds and its application to foliations

**大沢 健夫**(名古屋大学)Hodge theory with bounds and its application to foliations

### 2006/05/22

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

Uniformisation of Holomorphic Foliations by Curves I (Part II on May 29)

**Marco Brunella**(Bourgogne)Uniformisation of Holomorphic Foliations by Curves I (Part II on May 29)

[ Abstract ]

In the first lecture, we give a definition of "leaf" for a singular holomorphic one-dimensional foliation on a projective manifold. The definition is such that the leaves of a foliation glue together in a nice way, giving a "covering tube" which is a sort of semi-global flow box. This is, in some sense, the topological part of the theory. In the second lecture, we prove some convexity property of this covering tube. As a corollary we obtain that, when there are hyperbolic leaves, the leafwise Poincare' metric has some remarkable positivity property. In the third lecture, we study foliations all of whose leaves are parabolic. Using a suitable extension theorem for certain meromorphic maps, we show how to generalise the above positivity property to this degenerate class of foliations.

In the first lecture, we give a definition of "leaf" for a singular holomorphic one-dimensional foliation on a projective manifold. The definition is such that the leaves of a foliation glue together in a nice way, giving a "covering tube" which is a sort of semi-global flow box. This is, in some sense, the topological part of the theory. In the second lecture, we prove some convexity property of this covering tube. As a corollary we obtain that, when there are hyperbolic leaves, the leafwise Poincare' metric has some remarkable positivity property. In the third lecture, we study foliations all of whose leaves are parabolic. Using a suitable extension theorem for certain meromorphic maps, we show how to generalise the above positivity property to this degenerate class of foliations.

### 2006/05/22

15:00-16:30 Room #470 (Graduate School of Math. Sci. Bldg.)

Laminations with Singularities by Riemann Surfaces II

**Nessim Sibony**(Paris Sud)Laminations with Singularities by Riemann Surfaces II

### 2006/05/15

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

Laminations with Singularities by Riemann Surfaces I (Part II on May 22)

**Nessim Sibony**(Paris Sud)Laminations with Singularities by Riemann Surfaces I (Part II on May 22)

[ Abstract ]

The basic example of a lamination, possibly with singularites, by Riemann surfaces, is the closure of a leaf of a holomorphic foliation in the complex projective plane.There are also many examples arising from the theory of iteration of a holomorphic map. The goal is to introduce tools in order to understand the globalproperties of leaves of a holomorphic lamination, mostly in compact Kaehler manifolds. We will develop the following topics.

-Poincare metric on a hyperbolic lamination.

-Positive cycles and positive harmonic currents directed by a lamination.

-Ahlfors construction of positive harmonic currents.

-Cohomological and geometrical intersection of positive harmonic currents.

The basic example of a lamination, possibly with singularites, by Riemann surfaces, is the closure of a leaf of a holomorphic foliation in the complex projective plane.There are also many examples arising from the theory of iteration of a holomorphic map. The goal is to introduce tools in order to understand the globalproperties of leaves of a holomorphic lamination, mostly in compact Kaehler manifolds. We will develop the following topics.

-Poincare metric on a hyperbolic lamination.

-Positive cycles and positive harmonic currents directed by a lamination.

-Ahlfors construction of positive harmonic currents.

-Cohomological and geometrical intersection of positive harmonic currents.