## Seminar on Geometric Complex Analysis

Seminar information archive ～02/07｜Next seminar｜Future seminars 02/08～

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, Ryosuke Nomura |

**Seminar information archive**

### 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.

### 2006/05/08

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

Real-analytic Levi-flats in complex tori

**大沢 健夫**(名古屋大学)Real-analytic Levi-flats in complex tori

### 2006/04/24

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

Monge-Ampére mass at the boundary on some domains with corner

**Jonas Wiklund**(名古屋大学, JSPS fellow)Monge-Ampére mass at the boundary on some domains with corner

[ Abstract ]

The Monge-Ampére operator is a highly non-linear operator that assigns a positive measure to every plurisubharmonic function and the null-measure to every maximal plurisubharmonic measure, whenever it is well defined. We discuss the sweeping out of this measure to the boundary for functions that essentially vanish on the boundary, and show two examples that this boundary measure vanish outside the distinguished boundary. Namely for analytic polyhedrons and for the cross product of two hyperconvex domains. Some related open problems are also mentioned.

The Monge-Ampére operator is a highly non-linear operator that assigns a positive measure to every plurisubharmonic function and the null-measure to every maximal plurisubharmonic measure, whenever it is well defined. We discuss the sweeping out of this measure to the boundary for functions that essentially vanish on the boundary, and show two examples that this boundary measure vanish outside the distinguished boundary. Namely for analytic polyhedrons and for the cross product of two hyperconvex domains. Some related open problems are also mentioned.

### 2006/04/17

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

Dirichlet-to-Neumann map for Poincaré-Einstein metrics

**C. Robin Graham**(University of Washington)Dirichlet-to-Neumann map for Poincaré-Einstein metrics

[ Abstract ]

This talk will describe an analogue of a Dirichlet to Neumann map for Poincaré-Einstein metrics, also known as asymptotically hyperbolic Einstein metrics. An explicit identification of the linearization of the map at the sphere will be given for even interior dimensions, together with applications to the structure of the map near the sphere and to the positive frequency conjecture of LeBrun which was resolved by Biquard.

This talk will describe an analogue of a Dirichlet to Neumann map for Poincaré-Einstein metrics, also known as asymptotically hyperbolic Einstein metrics. An explicit identification of the linearization of the map at the sphere will be given for even interior dimensions, together with applications to the structure of the map near the sphere and to the positive frequency conjecture of LeBrun which was resolved by Biquard.

### 2006/01/30

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

Compact non-kaehler threefolds associated to hyperbolic 3-manifolds

**藤木 明**(大阪大学)Compact non-kaehler threefolds associated to hyperbolic 3-manifolds

### 2006/01/23

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

Stochastic processes and Besov spaces on local field

**金子 宏**(東京理科大)Stochastic processes and Besov spaces on local field

### 2005/12/05

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

Positive cones of hyper-Keahler manifold

**Sebastien Boucksom**(ParisVII / Univ. of Tokyo)Positive cones of hyper-Keahler manifold

### 2005/11/28

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

Schroeder equation and Abel equation

**上田哲生**(京都大学)Schroeder equation and Abel equation

### 2005/11/21

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

On CR-invariant differential operators

**Andreas Cap**(Univ. of Vienna)On CR-invariant differential operators

[ Abstract ]

My talk will be devoted to questions about differential operators which are intrinsic to non--degenerate CR structures of hypersurface type. Restricting to the subclass of spherical CR structures, this question admits an equivalent formulation in terms of representation theory, which leads to several surprising consequences.

Guided by the ideas from representation theory and using the canonical Cartan connection which is available in this situation, one obtains a construction for a large class of such operators, which continues to work for non--spherical structures, and even for a class of almost CR structures. In the end of the talk I will discuss joint work with V. Soucek which shows that in the integrable case many of the operators obtained in this way form complexes.

My talk will be devoted to questions about differential operators which are intrinsic to non--degenerate CR structures of hypersurface type. Restricting to the subclass of spherical CR structures, this question admits an equivalent formulation in terms of representation theory, which leads to several surprising consequences.

Guided by the ideas from representation theory and using the canonical Cartan connection which is available in this situation, one obtains a construction for a large class of such operators, which continues to work for non--spherical structures, and even for a class of almost CR structures. In the end of the talk I will discuss joint work with V. Soucek which shows that in the integrable case many of the operators obtained in this way form complexes.

### 2005/11/14

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

New invariants for CR and contact manifolds

**Raphael Pong**(Ohio State Univ)New invariants for CR and contact manifolds

[ Abstract ]

In this talk I will explain the construction of several new invariants for CR and contact manifolds as noncommutative residue traces of various geometric pseudodifferential projections. In the CR setting these operators arise from the ∂b-complex and include the Szegö projections. In the contact setting they stem from the generalized Szegö projections at arbitrary integer levels of Epstein-Melrose and from the contact complex of Rumin. In particular, we recover and extend recent results of Hirachi and Boutet de Monvel and answer a question of Fefferman.

In this talk I will explain the construction of several new invariants for CR and contact manifolds as noncommutative residue traces of various geometric pseudodifferential projections. In the CR setting these operators arise from the ∂b-complex and include the Szegö projections. In the contact setting they stem from the generalized Szegö projections at arbitrary integer levels of Epstein-Melrose and from the contact complex of Rumin. In particular, we recover and extend recent results of Hirachi and Boutet de Monvel and answer a question of Fefferman.

### 2005/11/07

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

Moduli of Galois coverings of the complex projective line

**難波誠**(追手門学院大学)Moduli of Galois coverings of the complex projective line

### 2005/10/24

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

Ambient metrics for even dimensional conformal structures

**平地健吾**(東大数理)Ambient metrics for even dimensional conformal structures

### 2005/10/17

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

On the discriminant of certain K3 surfaces

**吉川謙一**(東大数理)On the discriminant of certain K3 surfaces

### 2005/07/22

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

Szegö kernel の構成について

**倉西正武**(コロンビア大学)Szegö kernel の構成について

### 2005/07/22

15:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Effective Local Finite Generation of Multiplier Ideal Sheaves

**Dan Popovici**(JSPS, 名古屋大学多元数理)Effective Local Finite Generation of Multiplier Ideal Sheaves

### 2005/07/11

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

学習理論のゼータ関数と特異点解消

**青柳美輝**(上智大理工)学習理論のゼータ関数と特異点解消

### 2005/07/04

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

Variation of Bergman kernel of projective manifolds

**辻 元**(上智大理工)Variation of Bergman kernel of projective manifolds

### 2005/06/27

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

Uniqueness problem of analytic coverng spaces

**相原義弘**(沼津高専)Uniqueness problem of analytic coverng spaces

### 2005/06/06

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

Application of Hartogs type extension theorems to Levi flats in Kaehler manifolds

**大沢健夫**(名大多元数理)Application of Hartogs type extension theorems to Levi flats in Kaehler manifolds

### 2005/05/30

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

全曲率有限な完備極小曲面のガウス写像の除外値について

**宮岡礼子**(九大数理)全曲率有限な完備極小曲面のガウス写像の除外値について

### 2005/05/23

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

A-branes from CR-geometry

**赤堀隆夫**(兵庫県立大物質理学)A-branes from CR-geometry

### 2005/05/16

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

Algebraic degeneracy of holomorphic curves

**野口潤次郎**(東大数理)Algebraic degeneracy of holomorphic curves

### 2005/05/09

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

レビ形式が退化する、あるクラスの実超曲面の定義関数について

**林本厚志**(長野高専)レビ形式が退化する、あるクラスの実超曲面の定義関数について

### 2005/04/25

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

停留的写像類群とタイヒミュラー空間への作用

**藤川英華**(東工大情報理工)停留的写像類群とタイヒミュラー空間への作用