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Seminar information archive
Seminar information archive ～07/26｜Today's seminar 07/27 | Future seminars 07/28～
Lectures
17:30-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Antonio Degasperis (La Sapienza, University of Rome)
Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)
Antonio Degasperis (La Sapienza, University of Rome)
Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)
[ Abstract ]
A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.
A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.
Lectures
17:30-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Antonio Degasperis (La Sapienza, University of Rome)
Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)
Antonio Degasperis (La Sapienza, University of Rome)
Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)
[ Abstract ]
A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.
A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.
Lectures
09:45-10:45 Room #123 (Graduate School of Math. Sci. Bldg.)
Marzieh Forough (Ferdowsi Univ. Mashhad)
Stability of Fredholm property of regular operators on Hilbert $C^*$-modules (ENGLISH)
Marzieh Forough (Ferdowsi Univ. Mashhad)
Stability of Fredholm property of regular operators on Hilbert $C^*$-modules (ENGLISH)
Lectures
11:00-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Gerardo Morsella (Univ. Roma II)
Scaling algebras, superselection theory and asymptotic morphisms (ENGLISH)
Gerardo Morsella (Univ. Roma II)
Scaling algebras, superselection theory and asymptotic morphisms (ENGLISH)
Lectures
13:30-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Joav Orovitz (Ben-Gurion Univ.)
Tracially $\\mathcal{Z}$-absorbing $C^*$-algebras (ENGLISH)
Joav Orovitz (Ben-Gurion Univ.)
Tracially $\\mathcal{Z}$-absorbing $C^*$-algebras (ENGLISH)
Lectures
14:45-15:45 Room #118 (Graduate School of Math. Sci. Bldg.)
Nicola Watson (Univ. Toronto)
Noncommutative covering dimension (ENGLISH)
Nicola Watson (Univ. Toronto)
Noncommutative covering dimension (ENGLISH)
Lectures
16:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Marcel Bischoff (Univ. G\"ottingen)
Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)
Marcel Bischoff (Univ. G\"ottingen)
Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)
Lectures
17:15-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Hiroki Asano (Univ. Tokyo)
Group actions with Rohlin property (ENGLISH)
Hiroki Asano (Univ. Tokyo)
Group actions with Rohlin property (ENGLISH)
GCOE Seminars
16:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Marcel Bischoff (Univ. Göttingen)
Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-3.htm
Marcel Bischoff (Univ. Göttingen)
Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-3.htm
2013/01/28
Seminar on Geometric Complex Analysis
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)
Taiji MARUGAME (MS U-Tokyo)
Renormalized Chern-Gauss-Bonnet formula for complete Kaehler-Einstein metrics (JAPANESE)
Seminar on Probability and Statistics
13:00-14:10 Room #006 (Graduate School of Math. Sci. Bldg.)
Ernst August Frhr. v. Hammerstein (Albert-Ludwigs-Universität Freiburg)
Laplace and Fourier based valuation methods in exponential Levy models (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/13.html
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
Ernst August Frhr. v. Hammerstein (Albert-Ludwigs-Universität Freiburg)
Laplace and Fourier based valuation methods in exponential Levy models (JAPANESE)
[ Abstract ]
A fundamental problem in mathematical finance is the explicit computation of expectations which arise as prices of derivatives. Closed formulas that can easily be evaluated are typically only available in models driven by a Brownian motion. If one considers more sophisticated jump-type Levy processes as drivers, the problem quickly becomes rather nontrivial and complicated. Starting with the paper of Carr and Madan (1999) and the PhD thesis of Raible (2000), Laplace and Fourier based methods have been used to derive option pricing formulas that can be evaluated very efficiently numerically. In this talk we review the initial idea of Raible (2000), show how it can be generalized and discuss under which precise mathematical assumptions the Laplace and Fourier approach work. We then give several examples of specific options and Levy models to which the general framework can be applied to. In the last part, we present some formulas for pricing options on the supremum and infimum of the asset price process that use the Wiener-Hopf factorization.
FMSP Lectures
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
[ Reference URL ]A fundamental problem in mathematical finance is the explicit computation of expectations which arise as prices of derivatives. Closed formulas that can easily be evaluated are typically only available in models driven by a Brownian motion. If one considers more sophisticated jump-type Levy processes as drivers, the problem quickly becomes rather nontrivial and complicated. Starting with the paper of Carr and Madan (1999) and the PhD thesis of Raible (2000), Laplace and Fourier based methods have been used to derive option pricing formulas that can be evaluated very efficiently numerically. In this talk we review the initial idea of Raible (2000), show how it can be generalized and discuss under which precise mathematical assumptions the Laplace and Fourier approach work. We then give several examples of specific options and Levy models to which the general framework can be applied to. In the last part, we present some formulas for pricing options on the supremum and infimum of the asset price process that use the Wiener-Hopf factorization.
FMSP Lectures
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/13.html
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
GCOE Seminars
16:00-17:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Bernadette Miara (Universite Paris-Est)
The obstacle problem for a shallow membrane-Justification and stability (ENGLISH)
Bernadette Miara (Universite Paris-Est)
The obstacle problem for a shallow membrane-Justification and stability (ENGLISH)
[ Abstract ]
This lecture is twofold.
In the first part we recall the difference between the three-dimensional unilateral contact problem (the so-called Signorini problem) and its two-dimensional limit (the obstacle problem) in the case of an elastic shell as it was considered in [1] and [2].
In the second part we consider a simplified set of equations which describe the equilibrium equations of a shallow membrane (as justified in [3]) in contact with a plane obstacle and we study the stability of the contact zone with respect to small changes of the applied force, which amounts to studying the variation of the boundary of this contact zone. This kind of stability was first established in the scalar case for the Laplacian operator [4] then for the biharmonic operator [5]. The interest of the vectorial case considered here is due to the coupling effects between the in-plane and the transverse components of the displacement field in the framework of linearized Marguerre-von K´arm´an shell model.
This is a joint work with Alain L´eger, CNRS, Laboratoire de M´ecanique et d’Acoustique, 13402, Marseille, France.
This lecture is twofold.
In the first part we recall the difference between the three-dimensional unilateral contact problem (the so-called Signorini problem) and its two-dimensional limit (the obstacle problem) in the case of an elastic shell as it was considered in [1] and [2].
In the second part we consider a simplified set of equations which describe the equilibrium equations of a shallow membrane (as justified in [3]) in contact with a plane obstacle and we study the stability of the contact zone with respect to small changes of the applied force, which amounts to studying the variation of the boundary of this contact zone. This kind of stability was first established in the scalar case for the Laplacian operator [4] then for the biharmonic operator [5]. The interest of the vectorial case considered here is due to the coupling effects between the in-plane and the transverse components of the displacement field in the framework of linearized Marguerre-von K´arm´an shell model.
This is a joint work with Alain L´eger, CNRS, Laboratoire de M´ecanique et d’Acoustique, 13402, Marseille, France.
2013/01/26
Harmonic Analysis Komaba Seminar
13:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Guorong, Hu
(Tokyo Univesity) 13:30-15:00
On Triebel-Lizorkin spaces on Stratified Lie groups
(ENGLISH)
Profiles of solutions to an integral system related to
the weighted Hardy-Littlewood-Sobolev inequality
(JAPANESE)
Guorong, Hu
(Tokyo Univesity) 13:30-15:00
On Triebel-Lizorkin spaces on Stratified Lie groups
(ENGLISH)
[ Abstract ]
We introduce the notion of Triebel-Lizorkin spaces
$\\dot{F}^{s}_{p,q}(G)$ on a stratified Lie group $G$
in terms of a Littlewood-Paley-type decomposition
with respect to a sub-Laplacian $\\mathscr{L}$ of $G$,
for $s \\in \\mathbb{R}$, $0We show that the scale of these spaces is actually independent of
the precise choice of the sub-Laplacian
and the Littlewood-Paley-type decomposition.
As we shall see, many properties of the classical
Triebel-Lizorkin spaces on $\\mathbb{R}^{n}$, e.g.,
lifting property, embeddings and dual property,
can be extended to the setting of stratified Lie groups
without too much effort.
We then study the boundedness of convolution operators
on these spaces and finally,
we obtain a Hormander type spectral multipliers theorem.
Michiaki, Onodera (Kyushu University) 15:30-17:00We introduce the notion of Triebel-Lizorkin spaces
$\\dot{F}^{s}_{p,q}(G)$ on a stratified Lie group $G$
in terms of a Littlewood-Paley-type decomposition
with respect to a sub-Laplacian $\\mathscr{L}$ of $G$,
for $s \\in \\mathbb{R}$, $0We show that the scale of these spaces is actually independent of
the precise choice of the sub-Laplacian
and the Littlewood-Paley-type decomposition.
As we shall see, many properties of the classical
Triebel-Lizorkin spaces on $\\mathbb{R}^{n}$, e.g.,
lifting property, embeddings and dual property,
can be extended to the setting of stratified Lie groups
without too much effort.
We then study the boundedness of convolution operators
on these spaces and finally,
we obtain a Hormander type spectral multipliers theorem.
Profiles of solutions to an integral system related to
the weighted Hardy-Littlewood-Sobolev inequality
(JAPANESE)
[ Abstract ]
We study the Euler-Lagrange system for a variational problem
associated with the weighted Hardy-Littlewood-Sobolev inequality of
Stein and Weiss.
We show that all the nonnegative solutions to the system are radially
symmetric and have particular profiles around the origin and the
infinity.
This work extends previous results obtained by other authors to the
general case.
We study the Euler-Lagrange system for a variational problem
associated with the weighted Hardy-Littlewood-Sobolev inequality of
Stein and Weiss.
We show that all the nonnegative solutions to the system are radially
symmetric and have particular profiles around the origin and the
infinity.
This work extends previous results obtained by other authors to the
general case.
2013/01/25
Colloquium
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Mitsuhiro T. Nakao (Sasebo National College of Technology)
State of the art in numerical verification methods of solutions for partial differential equations (JAPANESE)
Mitsuhiro T. Nakao (Sasebo National College of Technology)
State of the art in numerical verification methods of solutions for partial differential equations (JAPANESE)
2013/01/24
GCOE Seminars
14:00-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Leevan Ling (Hong Kong Baptist University)
Global radial basis functions method and some adaptive techniques (ENGLISH)
Leevan Ling (Hong Kong Baptist University)
Global radial basis functions method and some adaptive techniques (ENGLISH)
[ Abstract ]
It is now commonly agreed that the global radial basis functions method is an attractive approach for approximating smooth functions. This superiority does not come free; one must find ways to circumvent the associated problem of ill-conditioning and the high computational cost for solving dense matrix systems.
In this talk, we will overview different variants of adaptive methods for selecting proper trial subspaces so that the instability caused by inappropriately shaped parameters were minimized.
It is now commonly agreed that the global radial basis functions method is an attractive approach for approximating smooth functions. This superiority does not come free; one must find ways to circumvent the associated problem of ill-conditioning and the high computational cost for solving dense matrix systems.
In this talk, we will overview different variants of adaptive methods for selecting proper trial subspaces so that the instability caused by inappropriately shaped parameters were minimized.
GCOE Seminars
15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Christian Clason (Graz University)
Parameter identification problems with non-Gaussian noise (ENGLISH)
Christian Clason (Graz University)
Parameter identification problems with non-Gaussian noise (ENGLISH)
[ Abstract ]
For inverse problems subject to non-Gaussian (such as impulsive or uniform) noise, other data fitting terms than the standard L^2 norm are statistically appropriate and more robust. However, these formulations typically lead to non-differentiable problems which are challenging to solve numerically. This talk presents an approach that combines an iterative smoothing procedure with a semismooth Newton method, which can be applied to parameter identification problems for partial differential equations. The efficiency of this approach is illustrated for the inverse potential problem.
For inverse problems subject to non-Gaussian (such as impulsive or uniform) noise, other data fitting terms than the standard L^2 norm are statistically appropriate and more robust. However, these formulations typically lead to non-differentiable problems which are challenging to solve numerically. This talk presents an approach that combines an iterative smoothing procedure with a semismooth Newton method, which can be applied to parameter identification problems for partial differential equations. The efficiency of this approach is illustrated for the inverse potential problem.
2013/01/23
Seminar on Mathematics for various disciplines
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Chun Liu (Pennsylvania State University)
Ionic Fluids and Their Transport: From Kinetic Descriptions to Continuum Models (ENGLISH)
Chun Liu (Pennsylvania State University)
Ionic Fluids and Their Transport: From Kinetic Descriptions to Continuum Models (ENGLISH)
[ Abstract ]
The problems of distribution and transport of charged particles and ionic fluids are ubiquitous in our daily life and crucial in physical and biological applications. The multiscale and multiphysics nature of these problems provides major challenges and motivations.
In this talk, I will present the derivation of the continuum models such as Poisson-Nerest-Planck (PNP) system from the kinetic formulations.
Our focus is on the multiple species solutions and the corresponding boundary conditions for bounded containers.
The problems of distribution and transport of charged particles and ionic fluids are ubiquitous in our daily life and crucial in physical and biological applications. The multiscale and multiphysics nature of these problems provides major challenges and motivations.
In this talk, I will present the derivation of the continuum models such as Poisson-Nerest-Planck (PNP) system from the kinetic formulations.
Our focus is on the multiple species solutions and the corresponding boundary conditions for bounded containers.
Operator Algebra Seminars
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
David Evans (Cardiff University)
Exotic subfactors and conformal field theories (ENGLISH)
David Evans (Cardiff University)
Exotic subfactors and conformal field theories (ENGLISH)
GCOE Seminars
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
David Evans (Cardiff University)
Exotic subfactors and conformal field theories (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
David Evans (Cardiff University)
Exotic subfactors and conformal field theories (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
GCOE Seminars
17:15-18:15 Room #370 (Graduate School of Math. Sci. Bldg.)
Volker Schulz (Trier University)
Shape and topology optimization in application (ENGLISH)
Volker Schulz (Trier University)
Shape and topology optimization in application (ENGLISH)
[ Abstract ]
Shape and topology optimization currently is of high interest for applications but also from a theoretical point of view. Recently, new developments in the shape calculus and in a related calculus for topology have enabled successful solutions of challenging optimization problems. This talk specifically reports on parameter free shape optimization in aerodynamics, thermoelastics and acoustics. Furthermore, novel results for the elastic topology optimization of the interior of wings are presented. We will try to give insight into the challenges in this field as well as the numerical solution approaches.
Shape and topology optimization currently is of high interest for applications but also from a theoretical point of view. Recently, new developments in the shape calculus and in a related calculus for topology have enabled successful solutions of challenging optimization problems. This talk specifically reports on parameter free shape optimization in aerodynamics, thermoelastics and acoustics. Furthermore, novel results for the elastic topology optimization of the interior of wings are presented. We will try to give insight into the challenges in this field as well as the numerical solution approaches.
2013/01/22
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Simon Goodwin (Birmingham University)
Representation theory of finite W-algebras (ENGLISH)
Simon Goodwin (Birmingham University)
Representation theory of finite W-algebras (ENGLISH)
[ Abstract ]
There has been a great deal of recent research interest in finite W-algebras motivated by important connection with primitive ideals of universal enveloping algebras and applications in mathematical physics.
There have been significant breakthroughs in the rerpesentation theory of finite W-algebras due to the research of a variety of mathematicians.
In this talk, we will give an overview of the representation theory of finite W-algebras focussing on W-algebras associated to classical Lie algebras (joint with J. Brown) and W-algebras associated to general linear Lie superalgebras (joint with J. Brown and J. Brundan).
There has been a great deal of recent research interest in finite W-algebras motivated by important connection with primitive ideals of universal enveloping algebras and applications in mathematical physics.
There have been significant breakthroughs in the rerpesentation theory of finite W-algebras due to the research of a variety of mathematicians.
In this talk, we will give an overview of the representation theory of finite W-algebras focussing on W-algebras associated to classical Lie algebras (joint with J. Brown) and W-algebras associated to general linear Lie superalgebras (joint with J. Brown and J. Brundan).
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Jarek Kedra (University of Aberdeen)
On the autonomous metric of the area preserving diffeomorphism
of the two dimensional disc. (ENGLISH)
Jarek Kedra (University of Aberdeen)
On the autonomous metric of the area preserving diffeomorphism
of the two dimensional disc. (ENGLISH)
[ Abstract ]
Let D be the open unit disc in the Euclidean plane and let
G:=Diff(D, area) be the group of smooth compactly supported
area-preserving diffeomorphisms of D. A diffeomorphism is called
autonomous if it is the time one map of the flow of a time independent
vector field. Every diffeomorphism in G is a composition of a number
of autonomous diffeomorphisms. The least amount of such
diffeomorphisms defines a norm on G. In the talk I will investigate
geometric properties of such a norm.
In particular I will construct a bi-Lipschitz embedding of the free
abelian group of arbitrary rank to G. I will also show that the space
of homogeneous quasi-morphisms vanishing on all autonomous
diffeomorphisms in G is infinite dimensional.
This is a joint work with Michael Brandenbursky.
Let D be the open unit disc in the Euclidean plane and let
G:=Diff(D, area) be the group of smooth compactly supported
area-preserving diffeomorphisms of D. A diffeomorphism is called
autonomous if it is the time one map of the flow of a time independent
vector field. Every diffeomorphism in G is a composition of a number
of autonomous diffeomorphisms. The least amount of such
diffeomorphisms defines a norm on G. In the talk I will investigate
geometric properties of such a norm.
In particular I will construct a bi-Lipschitz embedding of the free
abelian group of arbitrary rank to G. I will also show that the space
of homogeneous quasi-morphisms vanishing on all autonomous
diffeomorphisms in G is infinite dimensional.
This is a joint work with Michael Brandenbursky.
2013/01/21
Tuesday Seminar on Topology
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Naoki Kato (The University of Tokyo
)
Lie foliations transversely modeled on nilpotent Lie
algebras
(JAPANESE)
Naoki Kato (The University of Tokyo
)
Lie foliations transversely modeled on nilpotent Lie
algebras
(JAPANESE)
[ Abstract ]
To each Lie $\\mathfrak{g}$-foliation, there is an associated subalgebra
$\\mathfrak{h}$ of $\\mathfrak{g}$ with the foliation, which is called the
structure Lie algabra. In this talk, we will explain the inverse problem,
that is, which pair $(\\mathfrak{g},\\mathfrak{h})$ can be realized as a
Lie $\\mathfrak{g}$-foliation with the structure Lie algabra $\\mathfrak{h}
$, under the assumption that $\\mathfrak{g}$ is nilpotent.
To each Lie $\\mathfrak{g}$-foliation, there is an associated subalgebra
$\\mathfrak{h}$ of $\\mathfrak{g}$ with the foliation, which is called the
structure Lie algabra. In this talk, we will explain the inverse problem,
that is, which pair $(\\mathfrak{g},\\mathfrak{h})$ can be realized as a
Lie $\\mathfrak{g}$-foliation with the structure Lie algabra $\\mathfrak{h}
$, under the assumption that $\\mathfrak{g}$ is nilpotent.
Tuesday Seminar on Topology
17:30-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Tomohiko Ishida (The University of Tokyo)
Quasi-morphisms on the group of area-preserving diffeomorphisms of
the 2-disk
(JAPANESE)
Tomohiko Ishida (The University of Tokyo)
Quasi-morphisms on the group of area-preserving diffeomorphisms of
the 2-disk
(JAPANESE)
[ Abstract ]
Gambaudo and Ghys constructed linearly independent countably many quasi-
morphisms on the group of area-preserving diffeomorphisms of the 2-disk
from quasi-morphisms on braid groups.
In this talk, we will explain that their construction is injective as a
homomorphism between vector spaces of quasi-morphisms.
If time permits, we introduce an application by Brandenbursky and K\\c{e}
dra.
Gambaudo and Ghys constructed linearly independent countably many quasi-
morphisms on the group of area-preserving diffeomorphisms of the 2-disk
from quasi-morphisms on braid groups.
In this talk, we will explain that their construction is injective as a
homomorphism between vector spaces of quasi-morphisms.
If time permits, we introduce an application by Brandenbursky and K\\c{e}
dra.
Seminar on Geometric Complex Analysis
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)
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 $\rho_{f}\geq 2$.
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 $\rho_{f}\geq 2$.
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