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Seminar on Geometric Complex Analysis
Seminar information archive ～05/28｜Next seminar｜Future seminars 05/29～
| Date, time & place | Monday 10:30 - 12:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
Future seminars
2026/06/01
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Yohei Komori (Waseda Univ.)
Classification of arithmetic twice-punctured torus groups (Japanese)
https://forms.gle/8ERsVDLuKHwbVzm57
Yohei Komori (Waseda Univ.)
Classification of arithmetic twice-punctured torus groups (Japanese)
[ Abstract ]
A Fuchsian group is called arithmetic if it is commensurable with a Fuchsian group derived from a quaternion algebra. In this talk we will determine arithmetic twice-punctured torus groups; arithmetic once-punctured torus groups were already classified by Kisao Takeuchi. Our strategy is based on Takeuchi's approach to classify quadrilateral subgroups of the modular group. (“Subgroups of the modular group with signature (0 ; e1, e2, e3, e4)”（Saitama Math. Jour. Vol.14, 55—78, 1996).)
[ Reference URL ]A Fuchsian group is called arithmetic if it is commensurable with a Fuchsian group derived from a quaternion algebra. In this talk we will determine arithmetic twice-punctured torus groups; arithmetic once-punctured torus groups were already classified by Kisao Takeuchi. Our strategy is based on Takeuchi's approach to classify quadrilateral subgroups of the modular group. (“Subgroups of the modular group with signature (0 ; e1, e2, e3, e4)”（Saitama Math. Jour. Vol.14, 55—78, 1996).)
https://forms.gle/8ERsVDLuKHwbVzm57
2026/06/08
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Yoshihiko Matsumoto (The Univ. of Osaka)
CR-invariant energy of Legendrian knots in the Heisenberg group (Japanese)
https://forms.gle/8ERsVDLuKHwbVzm57
Yoshihiko Matsumoto (The Univ. of Osaka)
CR-invariant energy of Legendrian knots in the Heisenberg group (Japanese)
[ Abstract ]
We introduce an energy functional for Legendrian knots in the 3-dimensional Heisenberg group, which carries a natural contact structure. This is an analogue of the energy for ordinary knots in Euclidean 3-space due to O'Hara (1991). Whereas O'Hara's energy (more precisely, the one of exponent -2) is invariant under Möbius transformations, our energy for Legendrian knots is invariant under the action of PU(2,1), the group of CR automorphisms of the one-point compactification of the Heisenberg group. I would like to explain carefully how the energy should be defined so as to achieve the PU(2,1)-invariance, and how R-circles, a distinguished class of Legendrian (un)knots, arise as energy minimizers. Time permitting, I will also discuss some open problems. This talk is based on joint work with Jun O'Hara (Chiba University).
[ Reference URL ]We introduce an energy functional for Legendrian knots in the 3-dimensional Heisenberg group, which carries a natural contact structure. This is an analogue of the energy for ordinary knots in Euclidean 3-space due to O'Hara (1991). Whereas O'Hara's energy (more precisely, the one of exponent -2) is invariant under Möbius transformations, our energy for Legendrian knots is invariant under the action of PU(2,1), the group of CR automorphisms of the one-point compactification of the Heisenberg group. I would like to explain carefully how the energy should be defined so as to achieve the PU(2,1)-invariance, and how R-circles, a distinguished class of Legendrian (un)knots, arise as energy minimizers. Time permitting, I will also discuss some open problems. This talk is based on joint work with Jun O'Hara (Chiba University).
https://forms.gle/8ERsVDLuKHwbVzm57
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. )
TBA (Japanese)
[ Reference URL ]
https://forms.gle/8ERsVDLuKHwbVzm57
Online only. No in-person attendance.
Naoto Yotsutani (Shizuoka Univ. )
TBA (Japanese)
[ Reference URL ]
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)
TBA (Japanese)
[ Reference URL ]
https://forms.gle/8ERsVDLuKHwbVzm57
Shuho Kanda (The Univ. of Tokyo)
TBA (Japanese)
[ Reference URL ]
https://forms.gle/8ERsVDLuKHwbVzm57
