Seminar on Geometric Complex Analysis
Seminar information archive ~02/12|Next seminar|Future seminars 02/13~
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
2016/11/14
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Sachiko Hamano (Osaka City University)
(JAPANESE)
Sachiko Hamano (Osaka City University)
(JAPANESE)
2016/11/07
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hideyuki Ishi (Nagoya University)
(JAPANESE)
Hideyuki Ishi (Nagoya University)
(JAPANESE)
2016/10/31
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yutaka Ishii (Kyushu University)
(JAPANESE)
Yutaka Ishii (Kyushu University)
(JAPANESE)
2016/10/24
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Satoru Shimizu (Tohoku University)
Structure and equivalence of a class of tube domains with solvable groups of automorphisms (JAPANESE)
Satoru Shimizu (Tohoku University)
Structure and equivalence of a class of tube domains with solvable groups of automorphisms (JAPANESE)
[ Abstract ]
In the study of the holomorphic equivalence problem for tube domains, it is fundamental to investigate tube domains with polynomial infinitesimal automorphisms. To apply Lie group theory to the holomorphic equivalence problem for such tube domains $T_\Omega$, investigating certain solvable subalgebras of $\frak g(T_{\Omega})$ plays an important role, where $\frak g(T_{\Omega})$ is the Lie algebra of all complete polynomial vector fields on $T_\Omega$. Related to this theme, we discuss the structure and equivalence of a class of tube domains with solvable groups of automorphisms. Besides, we give a concrete example of a tube domain whose automorphism group is solvable and contains nonaffine automorphisms.
In the study of the holomorphic equivalence problem for tube domains, it is fundamental to investigate tube domains with polynomial infinitesimal automorphisms. To apply Lie group theory to the holomorphic equivalence problem for such tube domains $T_\Omega$, investigating certain solvable subalgebras of $\frak g(T_{\Omega})$ plays an important role, where $\frak g(T_{\Omega})$ is the Lie algebra of all complete polynomial vector fields on $T_\Omega$. Related to this theme, we discuss the structure and equivalence of a class of tube domains with solvable groups of automorphisms. Besides, we give a concrete example of a tube domain whose automorphism group is solvable and contains nonaffine automorphisms.
2016/10/17
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takaaki Nomura (Kyushu University)
(JAPANESE)
Takaaki Nomura (Kyushu University)
(JAPANESE)
2016/10/03
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hirokazu Shimauchi (Yamanashi Eiwa College)
Visualizing the radial Loewner flow and the evolution family (JAPANESE)
Hirokazu Shimauchi (Yamanashi Eiwa College)
Visualizing the radial Loewner flow and the evolution family (JAPANESE)
2016/06/27
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takayuki Koike (Kyoto University)
On a higher codimensional analogue of Ueda theory and its applications (JAPANESE)
Takayuki Koike (Kyoto University)
On a higher codimensional analogue of Ueda theory and its applications (JAPANESE)
[ Abstract ]
Let $Y$ be a compact complex manifold embedded in a complex manifold with unitary flat normal bundle. As a higher-codimensional generalization of Ueda's theory, we investigate the analytic structure of a neighborhood of $Y$. As an application, we give a criterion for the existence of a smooth Hermitian metric with semi-positive curvature on a nef line bundle.
Let $Y$ be a compact complex manifold embedded in a complex manifold with unitary flat normal bundle. As a higher-codimensional generalization of Ueda's theory, we investigate the analytic structure of a neighborhood of $Y$. As an application, we give a criterion for the existence of a smooth Hermitian metric with semi-positive curvature on a nef line bundle.
2016/06/20
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shin-ichi Matsumura (Tohoku University)
A transcendental approach to injectivity theorems for log canonical pairs (JAPANESE)
Shin-ichi Matsumura (Tohoku University)
A transcendental approach to injectivity theorems for log canonical pairs (JAPANESE)
2016/06/13
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Masanori Adachi (Tokyo University of Science)
(JAPANESE)
Masanori Adachi (Tokyo University of Science)
(JAPANESE)
2016/06/06
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shin Kikuta (Kogakuin University)
(JAPANESE)
Shin Kikuta (Kogakuin University)
(JAPANESE)
2016/05/30
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takeo Ohsawa (Nagoya University)
(JAPANESE)
Takeo Ohsawa (Nagoya University)
(JAPANESE)
2016/05/23
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Katsusuke Nabeshima (The University of Tokushima)
A computation method for algebraic local cohomology and its applications (JAPANESE)
Katsusuke Nabeshima (The University of Tokushima)
A computation method for algebraic local cohomology and its applications (JAPANESE)
[ Abstract ]
Local cohomology was introduced by A. Grothendieck. Subsequent development to a great extent has been motivated by Grothendieck's ideas. Nowadays, local cohomology is a key ingredient in algebraic geometry, commutative algebra, topology and D-modules, and is a fundamental tool for applications in several fields.
In this talk, an algorithmic method to compute algebraic local cohomology classes (with parameters), supported at a point, associated with a given zero-dimensional ideal, is considered in the context of symbolic computation. There are several applications of the method. For example, the method can be used to analyze properties of singularities and deformations of Artin algebra. As the applications, methods for computing standard bases of zero-dimensional ideals and solving ideal membership problems, are also introduced.
Local cohomology was introduced by A. Grothendieck. Subsequent development to a great extent has been motivated by Grothendieck's ideas. Nowadays, local cohomology is a key ingredient in algebraic geometry, commutative algebra, topology and D-modules, and is a fundamental tool for applications in several fields.
In this talk, an algorithmic method to compute algebraic local cohomology classes (with parameters), supported at a point, associated with a given zero-dimensional ideal, is considered in the context of symbolic computation. There are several applications of the method. For example, the method can be used to analyze properties of singularities and deformations of Artin algebra. As the applications, methods for computing standard bases of zero-dimensional ideals and solving ideal membership problems, are also introduced.
2016/05/16
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Masataka Tomari (Nihon University)
(JAPANESE)
Masataka Tomari (Nihon University)
(JAPANESE)
2016/05/09
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Atsushi Atsuji (Keio University)
Nevanlinna type theorems for meromorphic functions on negatively curved Kähler manifolds (JAPANESE)
Atsushi Atsuji (Keio University)
Nevanlinna type theorems for meromorphic functions on negatively curved Kähler manifolds (JAPANESE)
[ Abstract ]
We discuss a generalization of classical Nevanlinna theory to meromorphic functions on complete Kähler manifolds. Several generalization of domains of functions are known in Nevanlinna theory, especially the results due to W.Stoll are well-known. In general Kähler case the remainder term of the second main theorem of Nevanlinna theory usually takes a complicated form. It seems that we have to modify classical
methods in order to simplify the second main theorem. We will use heat diffusion to do that and show some defect relations. We would also like to give some Liouville type theorems for holomorphic maps by using similar heat diffusion methods.
We discuss a generalization of classical Nevanlinna theory to meromorphic functions on complete Kähler manifolds. Several generalization of domains of functions are known in Nevanlinna theory, especially the results due to W.Stoll are well-known. In general Kähler case the remainder term of the second main theorem of Nevanlinna theory usually takes a complicated form. It seems that we have to modify classical
methods in order to simplify the second main theorem. We will use heat diffusion to do that and show some defect relations. We would also like to give some Liouville type theorems for holomorphic maps by using similar heat diffusion methods.
2016/04/25
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Atsushi Yamamori (Academia Sinica)
The representative domain and its applications (JAPANESE)
Atsushi Yamamori (Academia Sinica)
The representative domain and its applications (JAPANESE)
[ Abstract ]
Bergman introduced the notion of a representative domain to choose a nice holomorphic equivalence class of domains. In this talk, I will explain that the representative domain is also useful to obtain an analogue of Cartan's linearity theorem for some special class of domains.
Bergman introduced the notion of a representative domain to choose a nice holomorphic equivalence class of domains. In this talk, I will explain that the representative domain is also useful to obtain an analogue of Cartan's linearity theorem for some special class of domains.
2016/04/18
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Kunio Obitsu (Kagoshima University)
(JAPANESE)
Kunio Obitsu (Kagoshima University)
(JAPANESE)
2016/04/11
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Taro Asuke (The University of Tokyo)
Defining the Julia sets on CP^2 (JAPANESE)
Taro Asuke (The University of Tokyo)
Defining the Julia sets on CP^2 (JAPANESE)
[ Abstract ]
The Julia sets play a central role in the study of complex dynamical systems as well as Kleinian groups where they appear as limit sets. They are also known to be meaningful for complex foliations without singularities, however still not defined for singular ones. In this talk, I will discuss some expected properties of the Julia sets for singular foliations and difficulties for defining them.
The Julia sets play a central role in the study of complex dynamical systems as well as Kleinian groups where they appear as limit sets. They are also known to be meaningful for complex foliations without singularities, however still not defined for singular ones. In this talk, I will discuss some expected properties of the Julia sets for singular foliations and difficulties for defining them.
2016/01/25
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Kunio Obitsu (Kagoshima Univ.)
(Japanese)
Kunio Obitsu (Kagoshima Univ.)
(Japanese)
2016/01/18
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hiroshige Shiga (Tokyo Institute of Technology)
Holomorphic motions and the monodromy (Japanese)
Hiroshige Shiga (Tokyo Institute of Technology)
Holomorphic motions and the monodromy (Japanese)
[ Abstract ]
Holomorphic motions, which was introduced by Mane, Sad and Sullivan, is a useful tool for Teichmuller theory as well as for complex dynamics. In particular, Slodkowski’s theorem makes a significant contribution to them. The theorem says that every holomorphic motion of a closed set on the Riemann sphere parametrized by the unit disk is extended to a holomorphic motion of the whole Riemann sphere parametrized by the unit disk. In this talk, we consider a generalization of the theorem. If time permits, we will discuss applications of our results.
Holomorphic motions, which was introduced by Mane, Sad and Sullivan, is a useful tool for Teichmuller theory as well as for complex dynamics. In particular, Slodkowski’s theorem makes a significant contribution to them. The theorem says that every holomorphic motion of a closed set on the Riemann sphere parametrized by the unit disk is extended to a holomorphic motion of the whole Riemann sphere parametrized by the unit disk. In this talk, we consider a generalization of the theorem. If time permits, we will discuss applications of our results.
2015/12/21
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Katsutoshi Yamanoi (Osaka Univ.)
On pseudo Kobayashi hyperbolicity of subvarieties of abelian varieties
(Japanese)
Katsutoshi Yamanoi (Osaka Univ.)
On pseudo Kobayashi hyperbolicity of subvarieties of abelian varieties
(Japanese)
[ Abstract ]
A subvariety of an abelian variety is of general type if and only if it is pseudo Kobayashi hyperbolic. I will discuss the proof of this result.
A subvariety of an abelian variety is of general type if and only if it is pseudo Kobayashi hyperbolic. I will discuss the proof of this result.
2015/12/14
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Fuminori Nakata (Fukushima Univ.)
Twistor correspondence for associative Grassmanniann
Fuminori Nakata (Fukushima Univ.)
Twistor correspondence for associative Grassmanniann
[ Abstract ]
It is well known that the 6-dimensional sphere has a non-integrable almost complex structure which is introduced from the (right) multiplication of imaginary octonians. On this 6-sphere, there is a family of psuedo-holomorphic $\mathbb{C}\mathbb{P}^1$ parameterised by the associative Grassmannian, where the associative Grassmaniann is an 8-dimensional quaternion Kaehler manifold defined as the set of associative 3-planes in the 7-dimensional real vector space of the imaginary octonians. In the talk, we show that this story is quite analogous to the Penrose's twistor correspondence and that the geometric structures on the associative Grassmaniann nicely fit to this construction. This is a joint work with H. Hashimoto, K. Mashimo and M. Ohashi.
It is well known that the 6-dimensional sphere has a non-integrable almost complex structure which is introduced from the (right) multiplication of imaginary octonians. On this 6-sphere, there is a family of psuedo-holomorphic $\mathbb{C}\mathbb{P}^1$ parameterised by the associative Grassmannian, where the associative Grassmaniann is an 8-dimensional quaternion Kaehler manifold defined as the set of associative 3-planes in the 7-dimensional real vector space of the imaginary octonians. In the talk, we show that this story is quite analogous to the Penrose's twistor correspondence and that the geometric structures on the associative Grassmaniann nicely fit to this construction. This is a joint work with H. Hashimoto, K. Mashimo and M. Ohashi.
2015/12/07
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Tatsuki Hayama (Senshu Univ.)
Cycle connectivity and pseudoconcavity of flag domains (Japanese)
Tatsuki Hayama (Senshu Univ.)
Cycle connectivity and pseudoconcavity of flag domains (Japanese)
[ Abstract ]
We consider an open real group orbit in a complex flag variety which has no non-constant function. We introduce Huckleberry's results on cycle connectivity and show that it is pseudoconcave if it satisfies a certain condition on the root system of the Lie algebra. In Hodge theory, we are mainly interested in the case where it is a Mumford-Tate domain. We also discuss Hodge theoretical meanings of this work.
We consider an open real group orbit in a complex flag variety which has no non-constant function. We introduce Huckleberry's results on cycle connectivity and show that it is pseudoconcave if it satisfies a certain condition on the root system of the Lie algebra. In Hodge theory, we are mainly interested in the case where it is a Mumford-Tate domain. We also discuss Hodge theoretical meanings of this work.
2015/11/30
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Jean-Pierre Demailly (Univ. de Grenoble I)
Extension of holomorphic functions defined on non reduced analytic subvarieties (English)
Jean-Pierre Demailly (Univ. de Grenoble I)
Extension of holomorphic functions defined on non reduced analytic subvarieties (English)
[ Abstract ]
The goal of this talk will be to discuss $L^2$ extension properties of holomorphic sections of vector bundles satisfying weak semi-positivity properties. Using techniques borrowed from recent proofs of the Ohsawa-Takegoshi extension theorem, we obtain several new surjectivity results for the restriction morphism to a non necessarily reduced subvariety, provided the latter is defined as the zero variety of a multiplier ideal sheaf. These extension results are derived from $L^2$ approximation techniques, and they hold under (probably) optimal curvature conditions.
The goal of this talk will be to discuss $L^2$ extension properties of holomorphic sections of vector bundles satisfying weak semi-positivity properties. Using techniques borrowed from recent proofs of the Ohsawa-Takegoshi extension theorem, we obtain several new surjectivity results for the restriction morphism to a non necessarily reduced subvariety, provided the latter is defined as the zero variety of a multiplier ideal sheaf. These extension results are derived from $L^2$ approximation techniques, and they hold under (probably) optimal curvature conditions.
2015/11/16
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hideki Miyachi (Osaka University)
Towards the complex geometry of Teichmuller space with extremal length (English)
Hideki Miyachi (Osaka University)
Towards the complex geometry of Teichmuller space with extremal length (English)
[ Abstract ]
In this talk, in aiming for studying a relation between the topological aspect and the complex analytical aspect of Teichmuller space, I will discuss a complex analytic property of extremal length functions. More precisely, I will give a concrete formula of the Levi form of the extremal length functions for ``generic” measured foliations and show that the reciprocal of the extremal length function is plurisuperharmonic. As a corollary, I will give alternate proofs of S. Krushkal results that the distance function for the Teichmuller distance is plurisubharmonic, and Teichmuller space is hyperconvex. If time permits, I will give a topological description of the Levi form with using the Thurston's symplectic form.
In this talk, in aiming for studying a relation between the topological aspect and the complex analytical aspect of Teichmuller space, I will discuss a complex analytic property of extremal length functions. More precisely, I will give a concrete formula of the Levi form of the extremal length functions for ``generic” measured foliations and show that the reciprocal of the extremal length function is plurisuperharmonic. As a corollary, I will give alternate proofs of S. Krushkal results that the distance function for the Teichmuller distance is plurisubharmonic, and Teichmuller space is hyperconvex. If time permits, I will give a topological description of the Levi form with using the Thurston's symplectic form.
2015/11/02
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shimobe Hirokazu (Osaka Univ.)
A class of non-Kahler manifolds (Japanese)
Shimobe Hirokazu (Osaka Univ.)
A class of non-Kahler manifolds (Japanese)
[ Abstract ]
We consider a special case of compact complex manifolds which are said to be super strongly Gauduchon manifolds. A super strongly Gauduchon manifold is a complex manifold with a super strongly Gauduchon metric. We mainly consider non-Kähler super strongly Gauduchon manifolds. We give a cohomological condition for a compact complex manifold to have a super strongly Gauduchon metric, and give examples of non-trivial super strongly Gauduchon manifolds from nil-manifolds. We also consider its stability under small deformations and proper modifications of super strongly Gauduchon manifolds.
We consider a special case of compact complex manifolds which are said to be super strongly Gauduchon manifolds. A super strongly Gauduchon manifold is a complex manifold with a super strongly Gauduchon metric. We mainly consider non-Kähler super strongly Gauduchon manifolds. We give a cohomological condition for a compact complex manifold to have a super strongly Gauduchon metric, and give examples of non-trivial super strongly Gauduchon manifolds from nil-manifolds. We also consider its stability under small deformations and proper modifications of super strongly Gauduchon manifolds.