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Seminar on Geometric Complex Analysis
Seminar information archive ～06/17｜Next seminar｜Future seminars 06/18～
| Date, time & place | Monday 10:30 - 12:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
Future seminars
2026/06/22
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Online only. No in-person attendance.
Naoto Yotsutani (Shizuoka Univ./IMAG, Univ. Montpellier)
Secondary polytopes of spherical varieties (Japanese)
https://forms.gle/8ERsVDLuKHwbVzm57
Online only. No in-person attendance.
Naoto Yotsutani (Shizuoka Univ./IMAG, Univ. Montpellier)
Secondary polytopes of spherical varieties (Japanese)
[ Abstract ]
This talk is based on ongoing joint work with Thibaut Delcroix and King Leung Lee. Our main objective is to investigate the Chow stability of spherical varieties.
A celebrated theorem of Gelfand, Kapranov, Sturmfels, and Zelevinsky (1992) states that the Chow polytopes of projective toric varieties coincide with their secondary polytopes. In the spherical setting, one can construct an analogous polytope, which may be viewed as a natural generalization of the secondary polytope of a toric variety. In this talk, I will explain the construction of this polytope and its relation to Chow stability. Particular emphasis will be placed on how the classical GKZ argument in the toric setting can be adapted to the broader context of spherical varieties.
[ Reference URL ]This talk is based on ongoing joint work with Thibaut Delcroix and King Leung Lee. Our main objective is to investigate the Chow stability of spherical varieties.
A celebrated theorem of Gelfand, Kapranov, Sturmfels, and Zelevinsky (1992) states that the Chow polytopes of projective toric varieties coincide with their secondary polytopes. In the spherical setting, one can construct an analogous polytope, which may be viewed as a natural generalization of the secondary polytope of a toric variety. In this talk, I will explain the construction of this polytope and its relation to Chow stability. Particular emphasis will be placed on how the classical GKZ argument in the toric setting can be adapted to the broader context of spherical varieties.
https://forms.gle/8ERsVDLuKHwbVzm57
2026/06/29
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Chin-Yu Hsiao (National Taiwan Univ.)
TBA (English)
[ Reference URL ]
https://forms.gle/8ERsVDLuKHwbVzm57
Chin-Yu Hsiao (National Taiwan Univ.)
TBA (English)
[ Reference URL ]
https://forms.gle/8ERsVDLuKHwbVzm57
2026/07/06
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Xiaojun Wu (Tsukuba Univ.)
TBA (English)
[ Reference URL ]
https://forms.gle/8ERsVDLuKHwbVzm57
Xiaojun Wu (Tsukuba Univ.)
TBA (English)
[ Reference URL ]
https://forms.gle/8ERsVDLuKHwbVzm57
2026/07/13
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Shuho Kanda (The Univ. of Tokyo)
Holomorphic polynomial crystallographic actions of nilpotent groups (Japanese)
https://forms.gle/8ERsVDLuKHwbVzm57
Shuho Kanda (The Univ. of Tokyo)
Holomorphic polynomial crystallographic actions of nilpotent groups (Japanese)
[ Abstract ]
It is a natural and still open question whether every simply connected nilpotent Lie group endowed with a left-invariant complex structure is biholomorphic to $\mathbb{C}^n$. In this talk, we give an affirmative answer under the additional assumption that the complex structure is nilpotent. Moreover, we construct such a biholomorphism explicitly by polynomial maps in exponential coordinates. As a consequence, every lattice in such a Lie group admits a free, properly discontinuous and cocompact action on $\mathbb{C}^n$ by holomorphic polynomial automorphisms. We interpret this as a holomorphic analogue of polynomial crystallographic actions, namely actions on $\mathbb{R}^n$ by polynomial diffeomorphisms that are free, properly discontinuous and cocompact, as introduced by Dekimpe, Igodt, and Lee.
[ Reference URL ]It is a natural and still open question whether every simply connected nilpotent Lie group endowed with a left-invariant complex structure is biholomorphic to $\mathbb{C}^n$. In this talk, we give an affirmative answer under the additional assumption that the complex structure is nilpotent. Moreover, we construct such a biholomorphism explicitly by polynomial maps in exponential coordinates. As a consequence, every lattice in such a Lie group admits a free, properly discontinuous and cocompact action on $\mathbb{C}^n$ by holomorphic polynomial automorphisms. We interpret this as a holomorphic analogue of polynomial crystallographic actions, namely actions on $\mathbb{R}^n$ by polynomial diffeomorphisms that are free, properly discontinuous and cocompact, as introduced by Dekimpe, Igodt, and Lee.
https://forms.gle/8ERsVDLuKHwbVzm57
