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

2013/01/28

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Taiji MARUGAME (MS U-Tokyo)
Renormalized Chern-Gauss-Bonnet formula for complete Kaehler-Einstein metrics (JAPANESE)

2013/01/21

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Takushi AMEMIYA (MS U-Tokyo)
Value distribution of meromorphic mappings to compact complex manifolds (JAPANESE)
[ Abstract ]
In a late paper of J. Noguchi and J. Winkelmann they showed the condition of being Kähler or non-Kähler of the image space to make a difference in the value distribution theory of meromorphic mappings into compact complex manifolds. In the present talk, we will discuss the order of meromorphic mappings to a Hopf surface which is more general than dealt with by Noguchi-Winkelmann, and an Inoue surface (they are non-Kähler surfaces). For a general Hopf surface $S$, we prove that there exists a differentiably non-degenerate holomorphic mapping $f:\mathbf{C}^2 \to S$ whose order satisfies $\rho_{f}\leq 1$. For an Inoue surface $S'$, we prove that every non-constant meromorphic mapping $f:\mathbf{C}^n \to S'$ is holomorphic and its order satisfies $\rho_{f}\geq 2$.

2012/12/17

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Hideaki Ikoma (Kyoto University)
On the existence of strictly effective basis on an arithmetic variety (JAPANESE)
[ Abstract ]
I would like to talk about some recent work of mine on the asymptotic behavior of the successive minima associated to a graded arithmetic linear series. A complete arithmetic linear series belonging to a hermitian line bundle on an arithmetic variety is defined as the Z-module of the global sections endowed with the supremum-norm, and the successive minima are invariants that measure the size of the sections with small norms.
If time permits, I would like to also explain some close relationship between the results and the general equi-distribution theory of rational points on an arithmetic variety.

2012/12/10

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Hiroshi Kaneko (Tokyo University of Science)
A Dirichlet space on ends of tree and Dirichlet forms with a nodewise orthogonal property (JAPANESE)

2012/12/03

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Yu Kawakami (Yamaguchi University)
On the geometric meaning of the maximal number
of exceptional values of Gauss maps for immersed surfaces in space forms
(JAPANESE)

2012/11/26

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Shin Nayatani (Nagoya University)
Quaternionic CR geometry (JAPANESE)

2012/11/19

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Yohei Komori (Waseda University)
On a degenerate family of Riemann surfaces of genus two over an elliptic curve (JAPANESE)
[ Abstract ]
We construct a degenerate family of Riemann surfaces of genus two constructed as double branched covering surfaces of a fixed torus. We determine its singular fibers and holomorphic sections.

2012/11/12

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
A.G. Aleksandrov (Institute of Control Sciences, Russian Acad. of Sci.)
Residues of meromorphic differential forms (ENGLISH)
[ Abstract ]
The purpose of the talk is to discuss several interesting aspects
of the classical residue theory originated by H. Poincar\\'e, J. de Rham and J. Leray and their followers. Focus topics of our studies are some of the less known applications, developed by the author in the past few years in complex analysis, topology and geometry of singular varieties and in the theory of differential equations. Almost all considerations are based essentially on properties of a special class of meromorphic differential forms called logarithmic or multi-logarithmic forms.

2012/10/29

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Atsushi Atsuji (Keio University)
Value distribution of meromorphic functions on foliated manifolds,II (JAPANESE)

2012/10/22

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Yusaku Tiba (Grad. School of Math. Sci., Univ. of Tokyo)
The second main therorem for entire curves into Hilbert modular surfaces (JAPANESE)

2012/10/15

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Takeo Ohsawa (Nagoya University)
An L^2 estimate on domains and application to Levi-flat surfaces (JAPANESE)

2012/07/09

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Tomoyuki Hisamoto (Univ. of Tokyo)
Volume of graded linear series and the existence problem of constant scalar curvature Kaehler metric (JAPANESE)
[ Abstract ]
We describe the volume of a graded linear series by the Monge-Ampere mass of the associated equilibrium metric. We relate this formula to the question whether the weak geodesic ray associated to a test configuration of given polarized manifold recovers the Donaldson-Futaki invariant.

2012/06/25

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Atsushi Hayashimoto (Nagano National College of Technology)
CR equivalence problem of CR manifolds with slice structure (JAPANESE)

2012/06/18

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
CR Q-curvature flow and CR Paneitz operator on 3-dimensional CR manifolds (JAPANESE)

2012/06/11

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Damian BROTBEK (University of Tokyo)
Differential forms on complete intersections (ENGLISH)
[ Abstract ]
Brückmann and Rackwitz proved a vanishing result for particular types of differential forms on complete intersection varieties. We will be interested in the cases not covered by their result. In some cases, we will show how the space $H^0(X,S^{m_1}\Omega_X\otimes \cdots \otimes S^{m_k}\Omega_X)$ depends on the equations defining $X$, and in particular we will prove that the theorem of Brückmann and Rackwitz is optimal. The proofs are based on simple, combinatorial, cohomology computations.

2012/06/04

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Sachiko HAMANO (Fukushima University)
Log-plurisubharmonicity of metric deformations induced by Schiffer and harmonic spans. (JAPANESE)

2012/05/28

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Shinichi TAJIMA (University of Tsukuba)
Local cohomology and hypersurface isolated singularities II (JAPANESE)
[ Abstract ]

・$\mu$-constant-deformation の Tjurina 数
・対数的ベクトル場の構造と構成法
・ニュートン非退化な超曲面に対する Kouchnirenko の公式
について述べる.

2012/05/21

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Shinichi TAJIMA (University of Tsukuba)
Local cohomology and hypersurface isolated singularities I (JAPANESE)

2012/05/14

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Hiroshi KANEKO (Tokyo University of Science)
Duality in the unit circle and the ring of p-adic intergers and van der Corput series (JAPANESE)

2012/05/07

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Yoshihiko Matsumoto (University of Tokyo)
The second metric variation of the total $Q$-curvature in conformal geometry (JAPANESE)
[ Abstract ]
Branson's $Q$-curvature of even-dimensional compact conformal manifolds integrates to a global conformal invariant called the total $Q$-curvature. While it is topological in two dimensions and is essentially the Weyl action in four dimensions, in the higher dimensional cases its geometric meaning remains mysterious. Graham and Hirachi have shown that the first metric variation of the total $Q$-curvature coincides with the Fefferman-Graham obstruction tensor. In this talk, the second variational formula will be presented, and it will be made explicit especially for conformally Einstein manifolds. The positivity of the second variation will be discussed in connection with the smallest eigenvalue of the Lichnerowicz Laplacian.

2012/04/16

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Yusuke Okuyama (Kyoto Institute of Technology)
Fekete configuration, quantitative equidistribution and wanderting critical orbits in non-archimedean dynamics
(JAPANESE)

2012/04/09

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Shigeharu TAKAYAMA (University of Tokyo)
Effective estimate on the number of deformation types of families of canonically polarized manifolds over curves
(JAPANESE)

2012/01/30

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Damian Brotbek (University of Tokyo)
Differential equations as embedding obstructions and vanishing theorems (ENGLISH)
[ Abstract ]
Given a smooth projective variety $X$ it is natural to wonder what is the smallest integer $N$ such that one can embed $X$ into $\mathbf{P}^N$. In this talk I will first recall what can be said for any smooth projective variety, then I will explain how the existence of some particular differential equations on $X$ yields obstructions to the existence of some projective embeddings.

2012/01/23

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Fuminori Nakata (Tokyo University of Science)
Twistor correspondence for R-invariant indefinite self-dual metric on R^4 (JAPANESE)

2012/01/16

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yu Kawakami (Yamaguchi University)
A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic 3-space (JAPANESE)
[ Abstract ]
We provide an effective ramification theorem for the ratio of canonical forms of weakly complete flat fronts in the hyperbolic 3-space. As an application, we give a simple proof of the classification of complete nonsingular flat surfaces in the hyperbolic 3-space.