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Seminar on Geometric Complex Analysis
Seminar information archive ～10/31｜Next seminar｜Future seminars 11/01～
| Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
Seminar information archive
2025/10/27
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shohei Ma (Institute of Science Tokyo)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Shohei Ma (Institute of Science Tokyo)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/10/20
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hideyuki Ishi (Osaka Metropolitan Univ.)
A CR-Laplacian type operator for the Silov boundary of a homogeneous Siegel domain (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Hideyuki Ishi (Osaka Metropolitan Univ.)
A CR-Laplacian type operator for the Silov boundary of a homogeneous Siegel domain (Japanese)
[ Abstract ]
Let $\Sigma$ be the Silov boundary of a homogeneous Siegel domain $D$ on which a Lie group $G$ acts transitively as affine transformations. The CR-structure on $\Sigma$ naturally induced from the ambient complex vector space is non-trivial if and only if $D$ is of non-tube type. In this case, $\Sigma$ is naturally identified with a two-step nilpotent Lie subgroup $N$ of $G$, called a generalized Heisenberg Lie group. Since the CR-structure is invariant under the action of $G$, the CR-cohomology space over $\Sigma$ can be regarded as a $G$-module. We consider unitarization of this presentation of $G$. The kernel of the CR-Laplacian does not give the solution because the natural Riemannian metric on $\Sigma$ is not $G$-invariant, so that the $G$-action does not preserve the space of CR-harmonic forms. Nevertheless, Nomura defined a unitary $G$-action on the space indirectly when $G$ is split solvable. In this talk, we introduce a space of CR-cochains with $G$-invariant inner product defined via the Fourier transform. Then the associated CR-operator is no longer a differential operator, while the kernel of the operator gives a unitarization of the representation of $G$ over the cohomology space.
[ Reference URL ]Let $\Sigma$ be the Silov boundary of a homogeneous Siegel domain $D$ on which a Lie group $G$ acts transitively as affine transformations. The CR-structure on $\Sigma$ naturally induced from the ambient complex vector space is non-trivial if and only if $D$ is of non-tube type. In this case, $\Sigma$ is naturally identified with a two-step nilpotent Lie subgroup $N$ of $G$, called a generalized Heisenberg Lie group. Since the CR-structure is invariant under the action of $G$, the CR-cohomology space over $\Sigma$ can be regarded as a $G$-module. We consider unitarization of this presentation of $G$. The kernel of the CR-Laplacian does not give the solution because the natural Riemannian metric on $\Sigma$ is not $G$-invariant, so that the $G$-action does not preserve the space of CR-harmonic forms. Nevertheless, Nomura defined a unitary $G$-action on the space indirectly when $G$ is split solvable. In this talk, we introduce a space of CR-cochains with $G$-invariant inner product defined via the Fourier transform. Then the associated CR-operator is no longer a differential operator, while the kernel of the operator gives a unitarization of the representation of $G$ over the cohomology space.
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/10/06
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yuya Takeuchi (Univ. of Tsukuba)
CR Paneitz operator on non-embeddable CR manifolds (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Yuya Takeuchi (Univ. of Tsukuba)
CR Paneitz operator on non-embeddable CR manifolds (Japanese)
[ Abstract ]
The CR Paneitz operator, a CR invariant fourth-order linear differential operator, plays a crucial role in three-dimensional CR geometry. It is closely related to global embeddability, the CR positive mass theorem, and the logarithmic singularity of the Szegő kernel. In this talk, I will discuss the spectrum of the CR Paneitz operator on non-embeddable CR manifolds, with particular emphasis on how it differs from the embeddable case.
[ Reference URL ]The CR Paneitz operator, a CR invariant fourth-order linear differential operator, plays a crucial role in three-dimensional CR geometry. It is closely related to global embeddability, the CR positive mass theorem, and the logarithmic singularity of the Szegő kernel. In this talk, I will discuss the spectrum of the CR Paneitz operator on non-embeddable CR manifolds, with particular emphasis on how it differs from the embeddable case.
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/07/07
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Taiji Marugame (The Univ. of Electro-Communications)
Chains on twistor CR manifolds and conformal geodesics in dimension three (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Taiji Marugame (The Univ. of Electro-Communications)
Chains on twistor CR manifolds and conformal geodesics in dimension three (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/06/23
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shoto Kikuchi (National Institute of Technology, Suzuka College)
Some properties of Azukawa pseudometrics for pluricomplex Green functions with poles along subvarieties (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Shoto Kikuchi (National Institute of Technology, Suzuka College)
Some properties of Azukawa pseudometrics for pluricomplex Green functions with poles along subvarieties (Japanese)
[ Abstract ]
The Azukawa pseudometric is defined as the difference between the pluricomplex Green function and its logarithmic term along each complex lines passing through a pole. Therefore, the Azukawa pseudometric is useful to study the behavior of the pluricomplex Green function around a pole. It is also known that the Azukawa pseudometric is closely related to several important objects in complex analysis, including the Crath\'{e}odory-Reiffen pseudometric, the Kobayashi-Reiffen pseudometric, the Bergman kernel, among others.
In this talk, we present some properties and applications of an analogue of the Azukawa pseudometric for the pluricomplex Green function with poles along subvarieties.
If time permits, I will also explain my recent studies related to this topic.
[ Reference URL ]The Azukawa pseudometric is defined as the difference between the pluricomplex Green function and its logarithmic term along each complex lines passing through a pole. Therefore, the Azukawa pseudometric is useful to study the behavior of the pluricomplex Green function around a pole. It is also known that the Azukawa pseudometric is closely related to several important objects in complex analysis, including the Crath\'{e}odory-Reiffen pseudometric, the Kobayashi-Reiffen pseudometric, the Bergman kernel, among others.
In this talk, we present some properties and applications of an analogue of the Azukawa pseudometric for the pluricomplex Green function with poles along subvarieties.
If time permits, I will also explain my recent studies related to this topic.
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/06/16
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Masakazu Takakura (Tokyo Metropolitan Univ.)
On the sharp $L^2$-estimate of Skoda division theorem (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Masakazu Takakura (Tokyo Metropolitan Univ.)
On the sharp $L^2$-estimate of Skoda division theorem (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/06/09
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Nobuhiro Honda (Institute of Science Tokyo)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Nobuhiro Honda (Institute of Science Tokyo)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/05/26
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shin-ichi Matsumura (Tohoku Univ.)
Fundamental groups of compact K\"ahler manifolds with semi-positive holomorphic sectional curvature (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Shin-ichi Matsumura (Tohoku Univ.)
Fundamental groups of compact K\"ahler manifolds with semi-positive holomorphic sectional curvature (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/05/19
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yu Yasufuku (Waseda Univ.)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yu Yasufuku (Waseda Univ.)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/05/12
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shuho Kanda (Univ. of Tokyo)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Shuho Kanda (Univ. of Tokyo)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/04/28
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Katsutoshi Yamanoi (Osaka Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Katsutoshi Yamanoi (Osaka Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/04/21
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Satoshi Nakamura (Institute of Science Tokyo)
Continuity method for the Mabuchi soliton on the extremal Fano manifolds (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Satoshi Nakamura (Institute of Science Tokyo)
Continuity method for the Mabuchi soliton on the extremal Fano manifolds (Japanese)
[ Abstract ]
We run the continuity method for Mabuchi's generalization of Kähler-Einstein metrics, assuming the existence of an extremal Kähler metric. It gives an analytic proof (without minimal model program) of the recent existence result obtained by Apostolov, Lahdili and Nitta. Our key observation is the boundedness of an energy functional along the continuity method. This talk is based on arXiv:2409.00886, the joint work with Tomoyuki Hisamoto.
[ Reference URL ]We run the continuity method for Mabuchi's generalization of Kähler-Einstein metrics, assuming the existence of an extremal Kähler metric. It gives an analytic proof (without minimal model program) of the recent existence result obtained by Apostolov, Lahdili and Nitta. Our key observation is the boundedness of an energy functional along the continuity method. This talk is based on arXiv:2409.00886, the joint work with Tomoyuki Hisamoto.
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/04/14
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hisashi Kasuya (Univ. of Nagoya)
Non-abelian Hodge correspondence and moduli spaces of flat bundles on Sasakian manifolds with fixed basic structures (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Hisashi Kasuya (Univ. of Nagoya)
Non-abelian Hodge correspondence and moduli spaces of flat bundles on Sasakian manifolds with fixed basic structures (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/01/06
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yongpan Zou (Univ. of Tokyo)
Positivity of twisted direct image sheaves (English)
https://u-tokyo-ac-jp.zoom.us/j/87229568765
Yongpan Zou (Univ. of Tokyo)
Positivity of twisted direct image sheaves (English)
[ Abstract ]
For a projective surjective morphism $f: X \to Y$ of complex manifolds with connected fibers, let $L$ be a line bundle on $X$. We are interested in the direct image $f_*(K_{X/Y} \otimes L)$. In general, the positivity of the bundle $L$ induces positivity in the direct image sheaves. Specifically, when $L$ is a big and nef line bundle, the vector bundle $f_*(K_{X/Y} \otimes L)$ is big. This is joint work with Y. Watanabe.
[ Reference URL ]For a projective surjective morphism $f: X \to Y$ of complex manifolds with connected fibers, let $L$ be a line bundle on $X$. We are interested in the direct image $f_*(K_{X/Y} \otimes L)$. In general, the positivity of the bundle $L$ induces positivity in the direct image sheaves. Specifically, when $L$ is a big and nef line bundle, the vector bundle $f_*(K_{X/Y} \otimes L)$ is big. This is joint work with Y. Watanabe.
https://u-tokyo-ac-jp.zoom.us/j/87229568765
2024/12/23
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Junjiro Noguchi (The Univ. of Tokyo)
Hyperbolicity and sections in a ramified cover over abelian varieties
with trace zero (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Junjiro Noguchi (The Univ. of Tokyo)
Hyperbolicity and sections in a ramified cover over abelian varieties
with trace zero (Japanese)
[ Abstract ]
We discuss a higher dimensional generalization of the Manin-Grauert Theorem ('63/'65) in relation with the function field analogue of Lang's conjecture on the finiteness of rational points in a Kobayashi hyperbolic algebraic variety over a number field. Let $B$ be a possibly open algebraic curve over $\mathbf{C}$, and let $\pi:X \to B$ be a smooth or normal projective fiber space. In '81 I proved such theorems for $\dim \geq 1$, assuming the ampleness of the cotangent bundle $T^*(X_t)$, and in '85 the Kobayashi hyperbolicity of $X_t$ with some boundary condition (BC) (hyperbolic embedding condition relative over $\bar{B}$).
It is interesting to study if (BC) is really necessary or not. If $\dim X_t=1$, (BC) is automatically satisfied, and if $T^*(X_t)$ is ample, (BC) is not necessary; thus in those cases, (BC) is unnecessary. Lately, Xie-Yuan in arXiv '23 obtained such a result without (BC) for $X$ which is a hyperbolic finite cover of an abelian variety $A/B$.
The aim of this talk is to present a simplified treatment of the Xie-Yuan theorem from the viewpoint of Kobayashi hyperbolic geometry. In particular, if the $K/\mathbf{C}$-trace $Tr(A/B)=0$ with $K=\mathbf{C}(B)$, there are only finitely many $X(K)$-points or sections in $X \to B$. In this case, Bartsch-Javanpeykar in arXiv '24 gave another proof based on Parshin's topological rigidity theorem ('90). We will discuss the proof which is based on the Kobayashi hyperbolicity.
[ Reference URL ]We discuss a higher dimensional generalization of the Manin-Grauert Theorem ('63/'65) in relation with the function field analogue of Lang's conjecture on the finiteness of rational points in a Kobayashi hyperbolic algebraic variety over a number field. Let $B$ be a possibly open algebraic curve over $\mathbf{C}$, and let $\pi:X \to B$ be a smooth or normal projective fiber space. In '81 I proved such theorems for $\dim \geq 1$, assuming the ampleness of the cotangent bundle $T^*(X_t)$, and in '85 the Kobayashi hyperbolicity of $X_t$ with some boundary condition (BC) (hyperbolic embedding condition relative over $\bar{B}$).
It is interesting to study if (BC) is really necessary or not. If $\dim X_t=1$, (BC) is automatically satisfied, and if $T^*(X_t)$ is ample, (BC) is not necessary; thus in those cases, (BC) is unnecessary. Lately, Xie-Yuan in arXiv '23 obtained such a result without (BC) for $X$ which is a hyperbolic finite cover of an abelian variety $A/B$.
The aim of this talk is to present a simplified treatment of the Xie-Yuan theorem from the viewpoint of Kobayashi hyperbolic geometry. In particular, if the $K/\mathbf{C}$-trace $Tr(A/B)=0$ with $K=\mathbf{C}(B)$, there are only finitely many $X(K)$-points or sections in $X \to B$. In this case, Bartsch-Javanpeykar in arXiv '24 gave another proof based on Parshin's topological rigidity theorem ('90). We will discuss the proof which is based on the Kobayashi hyperbolicity.
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/12/16
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Laurent Stolovitch (Universite Cote d'Azur)
CR singularities and dynamical systems (English)
https://forms.gle/gTP8qNZwPyQyxjTj8
Laurent Stolovitch (Universite Cote d'Azur)
CR singularities and dynamical systems (English)
[ Abstract ]
In this talk, we'll survey some recent results done since the seminal work of Moser and Webster about smooth real analytic surfaces in $C^2$ which are totally real everywhere but at a point where the tangent space is a complex line. Such a point is called a singularity of the Cauchy-Riemann structure. We are interested in the holomorphic classification of these surface near the singularity. It happens that there is a deep connection with holomorphic classification of some holomorphic dynamical systems near a fixed point so that new results for the later provide new result for the former.
[ Reference URL ]In this talk, we'll survey some recent results done since the seminal work of Moser and Webster about smooth real analytic surfaces in $C^2$ which are totally real everywhere but at a point where the tangent space is a complex line. Such a point is called a singularity of the Cauchy-Riemann structure. We are interested in the holomorphic classification of these surface near the singularity. It happens that there is a deep connection with holomorphic classification of some holomorphic dynamical systems near a fixed point so that new results for the later provide new result for the former.
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/12/09
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshiaki Suzuki (Niigata Univ.)
The spectrum of the Folland-Stein operator on some Heisenberg Bieberbach manifolds (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Yoshiaki Suzuki (Niigata Univ.)
The spectrum of the Folland-Stein operator on some Heisenberg Bieberbach manifolds (Japanese)
[ Abstract ]
.
[ Reference URL ].
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/12/02
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hideki Miyachi (Kanazawa Univ.)
Dualities in the $L^1$ and $L^\infty$-geometries in Teichm\”uller space (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Hideki Miyachi (Kanazawa Univ.)
Dualities in the $L^1$ and $L^\infty$-geometries in Teichm\”uller space (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/11/18
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yusaku Tiba (Ochanomizu Univ.)
Polarizations and convergences of holomorphic sections on the tangent bundle of a Bohr-Sommerfeld Lagrangian submanifold (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yusaku Tiba (Ochanomizu Univ.)
Polarizations and convergences of holomorphic sections on the tangent bundle of a Bohr-Sommerfeld Lagrangian submanifold (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/11/11
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takahiro Inayama (Tokyo University of Science)
Singular Nakano positivity of direct image sheaves (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Takahiro Inayama (Tokyo University of Science)
Singular Nakano positivity of direct image sheaves (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/10/28
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshihiko Matsumoto (Osaka Univ.)
. (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Yoshihiko Matsumoto (Osaka Univ.)
. (Japanese)
[ Abstract ]
.
[ Reference URL ].
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/10/21
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Atsushi Hayashimoto (National Institute of Technology Nagano College)
. (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Atsushi Hayashimoto (National Institute of Technology Nagano College)
. (Japanese)
[ Abstract ]
.
[ Reference URL ].
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/10/07
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shinichi Tajima (Niigata Univ.)
. (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Shinichi Tajima (Niigata Univ.)
. (Japanese)
[ Abstract ]
.
[ Reference URL ].
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/07/08
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Tomoyuki Hisamoto (Tokyo Metropolitan Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Tomoyuki Hisamoto (Tokyo Metropolitan Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/06/24
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Kazumasa Narita (Nagoya Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Kazumasa Narita (Nagoya Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
