## Seminar on Geometric Complex Analysis

Seminar information archive ～06/17｜Next seminar｜Future seminars 06/18～

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**

### 2010/10/18

13:00-14:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Degenerate complex Monge-Ampere equations (ENGLISH)

**Philippe Eyssidieux**(Institut Fourier, Grenoble)Degenerate complex Monge-Ampere equations (ENGLISH)

### 2010/10/04

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

The canonical coordinates associated to homogeneous Kaehler metrics on a homogeneous bounded domain (JAPANESE)

**Hideyuki ISHI**(Nagoya Univ)The canonical coordinates associated to homogeneous Kaehler metrics on a homogeneous bounded domain (JAPANESE)

[ Abstract ]

For a real analytic Kaehler manifold, one can define a canonical coordinate, called the Bochner coordinate, around each point. In this talk, we show that the canonical cooredinate is globally defined for a bounded homogeneous domain with a homogeneous Kaehler manifold, which is not necessarily the Bergman metric.

Then we obtain a standard realization of the homogeneous domain associated to the homogeneous metric.

For a real analytic Kaehler manifold, one can define a canonical coordinate, called the Bochner coordinate, around each point. In this talk, we show that the canonical cooredinate is globally defined for a bounded homogeneous domain with a homogeneous Kaehler manifold, which is not necessarily the Bergman metric.

Then we obtain a standard realization of the homogeneous domain associated to the homogeneous metric.

### 2010/07/12

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

The value distribution of the Gauss map of wave fronts and its applications (JAPANESE)

**Yu KAWAKAMI**(Kyushu Univ.)The value distribution of the Gauss map of wave fronts and its applications (JAPANESE)

### 2010/07/05

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

Expression of restricted volumes with current integration (JAPANESE)

**Shin-ichi MATSUMURA**(Univ. of Tokyo)Expression of restricted volumes with current integration (JAPANESE)

### 2010/06/28

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

Total Q-curvature vanishes on integrable CR manifolds (ENGLISH)

**Kengo HIRACHI**(Univ. of Tokyo)Total Q-curvature vanishes on integrable CR manifolds (ENGLISH)

### 2010/06/21

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

A remark on C^1 subharmonicity of the harmonic spans for discontinuously moving Riemann surfaces (JAPANESE)

**Sachiko HAMANO**(Fukushima Univ)A remark on C^1 subharmonicity of the harmonic spans for discontinuously moving Riemann surfaces (JAPANESE)

### 2010/06/14

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

Degeneracy condition for Levi form of distance to Levi flat real hypersurfaces in C^n (JAPANESE)

**Kazuko MATSUMOTO**(Osaka Prefecture University)Degeneracy condition for Levi form of distance to Levi flat real hypersurfaces in C^n (JAPANESE)

### 2010/06/07

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

Restricted Bergman kernel asymptotics (JAPANESE)

**Tomoyuki HISAMOTO**(Univ. of Tokyo)Restricted Bergman kernel asymptotics (JAPANESE)

### 2010/05/31

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

Singularities and analytic torsion (JAPANESE)

**Ken-ichi YOSHIKAWA**(Kyoto Univ.)Singularities and analytic torsion (JAPANESE)

### 2010/05/17

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

On the norm defined on the holomorphic maps of compact Riemann surfaces (JAPANESE)

**Masaharu TANABE**(Tokyo Inst. Tech.)On the norm defined on the holomorphic maps of compact Riemann surfaces (JAPANESE)

### 2010/05/10

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

Asymptotics of ACH-Einstein metrics, and an invariant tensor of partially-integrable almost CR manifolds (JAPANESE)

**Yoshihiko MATSUMOTO**(Univ. of Tokyo)Asymptotics of ACH-Einstein metrics, and an invariant tensor of partially-integrable almost CR manifolds (JAPANESE)

[ Abstract ]

To investigate strictly pseudoconvex partially-integrable almost CR manifolds as boundaries at infinity of noncompact complete Riemannian spaces, we study the Einstein equation for ACH metrics. At the jet level (of a certain order that depends only on the dimension) along the boundary, a solution uniquely exists up to the action of boundary-preserving diffeomorphisms. If we further consider higher-order solutions, without logarithmic singularities, in general we encounter an obstruction for construction, which is a local invariant tensor of the boundary. Some properties of that invariant tensor are also mentioned.

To investigate strictly pseudoconvex partially-integrable almost CR manifolds as boundaries at infinity of noncompact complete Riemannian spaces, we study the Einstein equation for ACH metrics. At the jet level (of a certain order that depends only on the dimension) along the boundary, a solution uniquely exists up to the action of boundary-preserving diffeomorphisms. If we further consider higher-order solutions, without logarithmic singularities, in general we encounter an obstruction for construction, which is a local invariant tensor of the boundary. Some properties of that invariant tensor are also mentioned.

### 2010/04/26

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

Deficiencies of holomorphic curves in projective algebraic varieties (JAPANESE)

**Yoshihiro AIHARA**(Fukushima Univ.)Deficiencies of holomorphic curves in projective algebraic varieties (JAPANESE)

### 2010/04/19

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

Loewner's theory on complex manifolds (ENGLISH)

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

**Filippo Bracci**(Universita di Roma, ``Tor Vergata'')Loewner's theory on complex manifolds (ENGLISH)

[ Abstract ]

Loewner's theory, introduced by Ch. Loewner in 1923 and developed later by Pommerenke, Kufarev, Schramm and others, has been proved to be a very powerful tool in studying extremal problems. In this talk we are going to describe a unified and general view of the deterministic Loewner theory both on the unit disc and on Kobayashi hyperbolic manifolds.

[ Reference URL ]Loewner's theory, introduced by Ch. Loewner in 1923 and developed later by Pommerenke, Kufarev, Schramm and others, has been proved to be a very powerful tool in studying extremal problems. In this talk we are going to describe a unified and general view of the deterministic Loewner theory both on the unit disc and on Kobayashi hyperbolic manifolds.

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

### 2010/04/12

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

Degeneracy of holomorphic curves into the complements of hypersurfaces in a complex projective space

[ Reference URL ]

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

**千葉 優作**(東大数理)Degeneracy of holomorphic curves into the complements of hypersurfaces in a complex projective space

[ Reference URL ]

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

### 2010/02/01

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

Connectedness of Levi nonflat pseudoconvex hypersurfaces in Kaehler manifolds

**大沢健夫**(名古屋大学多元数理科学研究科)Connectedness of Levi nonflat pseudoconvex hypersurfaces in Kaehler manifolds

### 2010/01/25

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

Eta invariant and Selberg Zeta function of odd type over convex co-compact hyperbolic manifolds

**Colin Guillarmou**(Ecole Normale Superieure)Eta invariant and Selberg Zeta function of odd type over convex co-compact hyperbolic manifolds

### 2010/01/18

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

スプライス商特異点について

**奥間智弘**(山形大学地域教育文化学部)スプライス商特異点について

### 2009/12/17

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Hyperbolicity of cycle spaces and automorphism groups of flag domains

**Alan Huckleberry**(Ruhr-Universität Bochum)Hyperbolicity of cycle spaces and automorphism groups of flag domains

### 2009/11/30

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

Equidistribution and Nevanlinna theory

**奥山裕介**(京都工芸繊維大学)Equidistribution and Nevanlinna theory

### 2009/11/16

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

Weighted Green functions of polynomial skew products on C^2

**上野康平**(京都大学大学院理学研究科)Weighted Green functions of polynomial skew products on C^2

### 2009/10/26

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

On Vojta's conjecture in the split function field case

**Pietro Corvaja**(Università di Udine)On Vojta's conjecture in the split function field case

### 2009/10/19

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

Variation formulas for principal functions (II)

**濱野佐知子**(松江高専)Variation formulas for principal functions (II)

### 2009/07/17

13:45-14:45 Room #128 (Graduate School of Math. Sci. Bldg.)

Logarthmic

Moduli Spaces for Surfaces of Class VII (joint work with M. TOMA)

**Karl Oeljeklaus**(University of Provence)Logarthmic

Moduli Spaces for Surfaces of Class VII (joint work with M. TOMA)

### 2009/07/17

15:00-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Boundary Regularity of d-bar Operator and Non Existence of Smooth Levi Flat Hypersurfaces in Compact K¥"ahler Manifolds

**Andrei Iordan**(Univ. Paris VI)Boundary Regularity of d-bar Operator and Non Existence of Smooth Levi Flat Hypersurfaces in Compact K¥"ahler Manifolds

### 2009/07/17

16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Holomorphic Dynamics In Several

Variables: equidistribution properties and statistical behavior

**Nessim Sibony**(Univ. Paris Sud)Holomorphic Dynamics In Several

Variables: equidistribution properties and statistical behavior