## Seminar on Geometric Complex Analysis

Date, time & place Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) Kengo Hirachi, Shigeharu Takayama, Ryosuke Nomura

Seminar information archive

### 2006/12/18

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

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

### 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

### 2006/11/27

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

### 2006/11/20

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

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

### 2006/11/06

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

### 2006/10/16

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

### 2006/07/03

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

### 2006/06/19

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

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

### 2006/06/05

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

### 2006/05/22

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

### 2006/05/22

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

### 2006/05/08

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

Real-analytic Levi-flats in complex tori

### 2006/04/24

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

### 2006/04/17

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

### 2006/01/30

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

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