Seminar on Geometric Complex Analysis

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Seminar information archive ～05/28｜Next seminar｜Future seminars 05/29～

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

2025/05/26

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

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

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

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

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)

[ 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 ]
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

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)

[ 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 ]
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)

[ 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 ]
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)

[ 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 ]
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)

[ 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

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

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

2024/10/28

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

[ 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)

[ 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

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

2024/06/17

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yuta Kusakabe (Kyushu Univ.)
Oka tubes in holomorphic line bundles (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8

2024/06/10

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Katsusuke Nabeshima (Tokyo Univ. of Science)
Computing Noetherian operators of polynomial ideals
--How to characterize a polynomial ideal by partial differential operators -- (Japanese)

[ Abstract ]
Describing ideals in polynomial rings by using systems of differential operators in one of the major approaches to study them. In 1916, F.S. Macaulay brought the notion of an inverse system, a system of differential conditions that describes an ideal. In 1937, W. Groebner mentioned the importance of the Macaulay's inverse system in the study of linear differential equations with constant coefficient, and in 1938, he introduced differential operators to characterize ideals that are primary to a rational maximal ideal. After that the important results and the terminology came from L. Ehrenpreise and V. P. Palamodov in 1961 and 1970, that is the characterization of primary ideals by the differential operators. The differential operators allow one to characterize the primary ideal by differential conditions on the associated characteristic variety. The differential operators are called Noetherian operators.
In this talk, we consider Noetherian operators in the context of symbolic computation. Upon utilizing the theory of holonomic D-modules, we present a new computational method of Noetherian operators associated to a polynomial ideal. The computational method that consists mainly of linear algebra techniques is given for computing them. Moreover, as applications, new computational methods of polynomial ideals are discussed by utilizing the Noetherian operators.

[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8

2024/05/27

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Taiji Marugame (The Univ. of Electro-Communications)
Hyperkähler ambient metrics associated with twistor CR manifolds (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8

2024/05/20

10:50-12:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Lijie Sun (Yamaguchi Univ.)
Kähler metrics in the Siegel domain (Japanese)

[ Abstract ]
The Siegel domain is endowed with an intrinsic Kähler structure, making it an exemplary model for the complex hyperbolic plane. Its boundary, characterized as the one-point compactification of the Heisenberg group, plays an important role in studying the geometry of the Siegel domain. In this talk, using the CR structure of the Heisenberg group we introduce a variety of Kähler structures within the Siegel domain. We conclude by demonstrating that all these metrics are PCR-Kähler equivalent, that is, essentially the same when confined to the CR structure. This talk is based on a joint work with Ioannis Platis and Joonhyung Kim.

[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8

2024/05/13

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yu Kawakami (Kanazawa Univ.)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8

2024/04/22

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takayuki Koike (Osaka Metropolitan Univ.)
Neighborhood of a compact curve whose intersection matrix has a positive eigenvalue (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8

2024/04/15

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yuya Takeuchi (Tsukuba Univ.)
Kohn-Rossi cohomology of spherical CR manifolds (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8

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Graduate School of Mathematical Sciences, The University of Tokyo

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